Shadow+Iron armor set - Initial Equipment
Simply non-impactful, with the Shadow set being better IIRC than the Iron set (then again Kain has Jump, so it's a wash). One of the rare underrated weapons is the Spear, since it gives Kain 99% hit rate.. and unless he's in the back row (and not Jumping), he's technically doing a lot more reliable damage than Cecil will up to a certain point.
The dark knight equipment being to similar to the normal equipment has always bothered me. Everything storyline-wise tells you that dark knights are supposed to be incredibly powerful, yet in-game it never really shows for Cecil unless he's stuck in a party of mages (Which he is the majority of the time you have him). Of course you don't want to make him too overpowered, but it would've been nice if the dark gear had higher magic defense and holy resistance or something.
Interestingly they gave dark knight Cecil the ability to equip the iron shield in the DS version but none of the other iron equipment. At first I thought it was a simple mistake, but it turns out the two dark shields are holy resistant (And as such weak against dark), they probably expected you to use the iron shield when facing undead. I never bothered confirming if the undead in the DS version attack with dark or not, my guess is they do, I'll look into it next playthrough.
Rydia's initial equipment + Weapon+Armor shops @ Kaipo...
Rydia already has optimal equipment, but won't be able to take advantage of the armor's evasion until her Agility is at 8. The Rod has a decent initial weapon-spell, which has a decent initial spell power, but has a 1x spell multiplier. This can still be stronger than the other elemental Rods when it is vs magic defense, which tends to actually increase overtime with newer monsters, unlike defense. The Bow+Arrow setup is only there for Rosa, unless you like torturing yourself. The Staff is also completely useless, since Poison status isn't exploited until Milon-Z/Scamaglione (undead version). I'm surprised they never made this a White Magic spell. The other strange thing is why the hell are they selling the Cloth Robe... when it has no positive attributes over the Leather Robe...
The only logical reason I see for selling the cloth/clothing is for completeness. Similar to the iron equipment at Agart although one could argue that was intended for Cid...ignoring the fact that the stuff at Baron is far better for him.
Cave of the Octomammoth..
IceRod - Once in a blue moon, you may want to try your luck with Rydia hitting, but it's best when she has at least a 2x attack multiplier to increase the chances of a hit. At least you have an alternative to cast a kinda weak Ice-1, but it has a better spell multiplier.. even though the spell power of Ice 1 is weak. It depends whether you want concentrated fire with the Rod vs the potential split damage that the IceRod can provide.. which can be useful for eliminating Zombies which tend to survive a pathetic Tellah's Fire1 or Cure2.
Silver Ring - If you're fortunate, you may get this via a drop by the TinyMage. This has actual impact once you get it, since there are a number of Spirit enemies you face before being able to buy this @ Mysidia.
Leather Hat - One of the few peeves I have is that this armor is only findable early on, yet buyable @ Toroia of all places... it bothers me when the early party is put in a really bad position of "who gets the crappy Cap".
Darkness equipment set - I've got lots of meh, although the weapon is probably the most impactful of them all.
The only time I attack with the ice rod is against turtles/adamantoises, its anti-reptile property can take them down very quickly if you get a good whack on them.
"who gets the crappy Cap"

The darkness/Hades set should have come with some other resistance, maybe fire for those pesky spirits (Or ice if you're going for the "Cecil sucks here" angle). I don't know why they ditched the darkness status on the darkness sword/shadowblade, I can't really see it making the weapon too powerful.
At the Spoony Bard's Domain..
RubyRing - This is a good time to just store them up.. though I can't say it's that useful.. until version 2 of the Dark Elf's battle.. which is most likely when you are not equipping this piece of equipment. I get the feeling this ring needs a stat boost, other than the rarely used Piggy status...
CrossBow - Just for Rosa please.
Bard's Robe - Initially, I thought it was a good idea to just sell this... after finding out it provides Silence resistance.. I was a tad reluctant to do so. There isn't really a technical merit for keeping it over the Leather Robe, but for the small chance that you want Edward to keep singing, Silence protection should be there. It probably needs a stat boost though...
You know, every playthrough I hold onto that bard's tunic and never bother actually using it. Lilith is (Probably, I may have forgotten some) the only enemy that can silence you before you have access to rune rings, and she's rare enough that I don't bother equipping it on the mountain.
Yang and "The Claw"
Sometimes it seems annoying, but having the FireClaw is great because his hit rate increases, but there are a few monsters that simply aren't receptive to that attack (damn you Spirits+Souls). Oh well, no big deal I guess.
Once you are able to buy the Black armor set and the oddly priced Claws.. especially when they don't have varying hit rates or anything to justify price differences... it's another meh.
Black Sword/Deathbringer - Great weapon, kills everything that's "underleveled". It's a great weapon to bond with Twins when you're exposing the area north of Mt. Ordeals.
Generally I have the fire claw on Yang unless I have a good reason to be using something else. Early on I got myself convinced that it was stronger than the others and that habit stuck long after I learned that it wasn't.

The Town With the Awesome Theme
Paladin equipment set - It would've been nice if they hinted that you should buy this stuff before going up the mountain.. so idiots would not have a right to be stupid. There's only a few peeves that I have with this set, primarily because the next set (the Silver/Mythril set) is effectively the most useless armor set in the game, and I've explained why on the monster type distribution argument thread I wrote a while back. Spirit protection is great if.. you fight them more often than not.
Gaea Hat - This arguably is better than the Paladin Hat... you get evasion, an additional boost to Wisdom/Intelligence (for more magic evasion), and magic defense over the meh-for-defense.
Gaea Robe - I'm not sure who wrote the fucking manual, but it's protection is against gradual petrification... this would've been nice if that was available before Mt. Hobs where the Cockatrice is worth fearing.
Holy Arrows - These are possibly most underrated arrows that people don't bother using for the Twins. They are worth their usage (and it's all fucked up in FF4A anyways) all will mow everything down, minus the Liliths. These become temporarily useless at the Baron Waterway...
Cure Staff - It's better than seeing Tellah fight.. make him and maybe Porom useful.. and play more defensively/conservative if you like to keep guys alive.
Flame Rod - An increased spell multiplier (3x), but it will take some time to kill certain monsters, minus the monsters that absorb this.. either way, you have a choice between reliability vs insta-kill gambles with the Bow+Arrow setup.
If said idiots can't piece together "I'm supposed to climb up the mountain to become a paladin, maybe this
paladin equipment would be useful for the return trip..." then they don't deserve to be playing this great game.

They have slightly more of an excuse in any version that isn't FF2us or FF4 PSX because the item names are a bit less descriptive. Only a bit though, "light/lustrous" and "knight's" are more than enough to tip me off that that stuff is intended for a holy knight, if the other three pieces are the gauntlets probably are as well.
The gaia gear...to be honest I never even realized it prevented gradual petrification until I read it in a walkthrough years after I started playing the game. There are a number of places it's useful, but old habits die hard and I usually forget about equipping it.
I usually go the flame rod and healing staves route, although sometimes I'll give Porom the crossbow and holy arrows. They made the Heal spell's animation ridiculously slow in the DS version, to the point I swear they did it on purpose so you didn't spam it every turn, it's about twice as slow as Cure's animation, maybe worse...
Back @ Baron...
Tiara - Taking that extra trip to Mist is worth it. Obviously this is best used on Rydia, but the added extra defense (magic too) with Dragon resistance (which starts being useful at the Tower of Bab-il via Cave Eblana) and Lightning resistance (which is also a benefit vs the same monster) cannot be understated.
Change Rod - This is the best monster neutralizer. It's obviously not going to work for every monster, but since weapon-magic is nearly realiable, you can't really argue against it, plus it makes Tellah a better Black Magic user (to actual reasonable levels).
Whip - Meh since Rydia comes back with one.
Dancing Dagger - This has a decent life span until you reach Tomra. The simple fact this weapon-spell ignores Reflect and has a reasonable better spell power base than the elemental Rods but not the level 2 elementals is a nice boost.
Thunder Rod - Meh, a 4x spell multiplier doesn't give me any "shock" value. It doesn't have the same impact that the Dancing Dagger has.
Karate Robe - Although expensive, it is the best armor available for the Magnetic Cave. You can easily justify the value over the lacking Gaea Robes.. but it won't beat out the Paladin Armor IMO. Besides, it's cheaper that way. Once the twins leave, the extra pair of Robes will go to Cid and Cecil.. which is financially sane. The Strength Boost is a nice bonus.
Headband - This is one of the few pieces of equipment that one should considering buying a set for the entire party. Charm protection is worth the price. The nifty Strength bonus is even better, and this piece of equipment easily beats out the Leather Cap when you are considering equipment options for the Magnetic Cave. In fact, you combine the Karate Robe with the Headband, you get an insta-attack multiplier boost.
Ancient Sword - The only letdown is that this weapon should at least attempt to be stronger than the Legend Sword.. since the status afflication doesn't provide impact until the next attack.
It's a damn shame the change/polymorph rod is all but useless in the DS version. My favorite thing about it is that it's only good for nullifying magical attacks, physicals are just as dangerous as before, which prevents it from being overpowered.
The whip may have been useful if Porom could equip it, as you already mentioned the holy arrows aren't very good in the waterway and staves are garbage. The healing staff's Heal spell is really getting worthless at this point.
The dancing dagger is awesome...perhaps too awesome. It pretty much replaces Rydia's attack command (Mine literally did in the DS version) until Tomra as you say. Maybe that's not a fault with the dagger but with the other equipment.
I've never even bothered with the ancient sword, it's just not worth the attack power reduction.
Once You Get the Airship...
Elemental Arrows - They are not impactful for the Magnetic Cave, despite being stronger in attack power. Holy Arrows hold their own much better.
GreatBow - It's reasonable at this point of the game to use, and it's fairly reliable.
Silver Armor Set - Virtually useless set, as the defensive boosts are of minimal impact IMO.
Silver Weapon Set - Most of these are useless.. the Knife is a nice throwaway weapon, the Staff heals like the Unicorn Horn (which is nothing worth speaking of), the Sword is surpassed by the Slumber Sword easily, and the Hammer is a nice bump.. but if the Wooden Hammer kept its Lit-2 weapon-spell property, ths Silver Hammer would be useless to me. In fact, it would make the trek through the Tower of Zot much easier (especially with the Pudding/Flan monsters).
*Hand Axe - Although this was never included in the original, after testing this out in Paladin's hack, I believe this weapon sucks if it was inserted in this scenario (it would suck more than the Legend Sword too).. primarily because of its shit-for-hit-rate. This weapon is not better than the original Wooden Hammer, and it's metallic to boot.. so even if you have Cid with the best defense, he couldn't hit a lick.
Ah, so I'm not the only one who goes through there with holy arrows. Again I had this incorrect notion that fire was somehow the best of the three for the longest time.
FF4 DS makes that place painful for Cecil...because he can't use a bow
or a staff he's stuck using elemental "shards," tiny wooden daggers which have 5 attack power. I completely forgot to check if they can cast magic or not, that might be their one saving grace, otherwise they're just garbage.
The whole silver/mythril weapon set is utterly worthless, the only one I could justify buying would be the hammer, and even that's not really worth it. Same goes for the armor for the most part, this needs some huge advantage over the paladin gear if they want me to use it.