Keep in mind, these are just my opinions. If you like an item I don't use then that's your individual way of playing the game. The analysis is more there to A) give some more life to the segment and B) show people how I play the game.
For a comparative list of who makes what item and for how much, as well as cost effective Item Creation tips, refer to this page.
Used to heal injuries and status. Pretty much vital to most players, since even if you're good enough to keep Ark safe there are times the pioneers will be taking damage and unable to fight back (either by having no fighters in the group or when there's a sniping CIMA attacking from a distance). Jean is usually your best bet for making most of these, however Eberle isn't much worse and will definitely do until he joins.
Potion A (ポーション A Pooshon): Restores 10 HP
Use or Toss...Since some characters have less than fifteen HP, they'll probably be full when their AI decides to use this. Plus, they work well for general use, as Jean and Eberle can make them for real cheap. But after a certain point in time, they just don't pull it for boss fights anymore.
Potion B (ポーション B Pooshon): Restores All HP
Use or Toss...Unless you have a perfect record of not being hit, then this is practically a must have later in the game. Due to their high cost of manufacturing, even with Jean, you'd probably want to save them for boss monsters. I think I start equipping them by either Air Garden or Lonely Factory.
Potion C (ポーション C Pooshon): Restores 10 HP to all.
Use or Toss...If I find them, I keep them for the few times a great number of my pioneers are put in danger with no way of preventing them from getting hurt for an extended period of time. But I never make them, since normally the few points of damage they receive can be cured by a game of Pass the Heal Ring.
Restore (リストア Risutoa): Cures negative status.
Use or Toss...I rarely need them since the only status effect I generally worry about is Poison and I just give both Ark and Ivy Poison Blocks. It's only before Ivy gets her amulet (the first can be found in Beginning World, prior to encountering a poison CIMA) and the occasional hit on a pioneer (especially in splits) that I need them. For all other status, I simply waste time standing by Eberle and/or Jean, letting a round of Pass the Heal Ring fix my team back to full.
These have several effects used to turn the tide of battle by hurling them at CIMA. Good if you're the type who likes setting traps or prefers fighting from a distance with short-ranged Ark, but if you just like hacking your way through they might not interest you as much. Not gonna repeat my analysis of these, so just know that the game can be beaten without any of them.
The Bs of these series' are extremely overpowered...but the Majesty cost to make them is exorbitantly high in return.
Bomb A (ボム A Bomu): Throw it to cause about 5 points of damage. Can sometimes double hit the enemy if they stay in the blast.
Bomb B (ボム B Bomu): Throw it to cause about 10 points of damage. Can sometimes double hit the enemy if they stay in the blast.
Shake A (シェイク A Sheiku): Causes a quake, inflicting about 3-6 damage to all visible enemies.
Shake B (シェイク B Sheiku): Causes a quake, inflicting incredibly large amounts of damage to all visible enemies. I've gotten as little as 12 damage and as high as like 18 when using this item.
Mine A (マイン A Main): Sets a trap that explodes when an enemy steps on it, causing 5 points of damage. Can sometimes double hit the enemy if they stay in the blast.
Mine B (マイン B Main): Sets a trap that explodes when an enemy steps on it, causing 10 points of damage. Can sometimes double hit the enemy if they stay in the blast.
Smoke (スモーク Sumooku): Confuses enemies.
Though situational, they can turn the tide of battle if used right. One is practically necessary to not watch your pioneers die slow and painful deaths, while one of the others is a godsend on the first boss. The others are still good in certain context, but in no means necessary.
Material (マテリアル Materiaru): Can upgrade armor and weapons with Doug.
Use or Toss...Unless you're doing a challenge playthrough where you forbid enhancements, it's probably one of the more important items you'll find.
96 of these little buggers exist, hidden in the dungeons of the game and in Doug and Ileyda's inventories by default. That's enough to upgrade everyone's weapons and armor to full (16 groups of 4 armor + 8 groups of 4 weapon = 24 groups of 4 = 96 Materials).
Power Up (パワー アップ Pawaa Appu): Increases attack by one point for a short time (i.e. Ark has a base attack of 5 and can do 2 damage vs a Rog, using this makes it 6 and he can do 3 damage vs a Rog; if his base attack is 6 and he can do 3 damage vs a Rog, this makes it 7 so he can do 4 damage vs a Rog).
Use or Toss...While I never make this, once in awhile I'll save one that I found and bean on the boss with it. But usually I just stick to regular combat and recycle them. One HP more of damage isn't worth it in my book.
All Dash (オール ダッシュ Ooru Dasshu): Entire party moves faster.
Use or Toss...Since the only people I worry about speed with have Speed Rings, I only use it in instances where I need to go fast to avoid traps: spikes coming up at set intervals, fireballs raining down on the enemy, timed gates (especially when sniping CIMA are attacking at the same time). It would be an expensive prospect to create enough to go through every floor of every dungeon.
Lightning (サンダ Sanda): Can be used by Ark, Vanrose and Doug. Enchants sword to shoot beams of lightning at enemies. Dissipates when the user is hit. It is called "Thunder" in the Japanese version.
Use or Toss...Practically vital to beating Bruton, the first boss, as getting close to that thing'll get you killed. You probably won't need more than you start with, if you nab Vanrose and Doug's before the split, and after Bruton falls you may never use it again. Though post-Silver Snow uses may include being able to hit from afar and making crack imitations of Link.
Speed Shot (スピード ショット Supiido Shotto): Can be used by Ivy, Halley, Shelley and Jean. Rapid fires a gun for multiple shots with one press of the button. Dissipates when the user is hit.
Use or Toss...Since I use Ark in all important context, I just toss the thing. I guess if I was really bored when I was controlling one of the long range attackers...
Pigeons (ピジョン Pijon): Can be used by Rick. A pair of pigeons circle around him, acting as both a barrier and a weapon to attack enemies that get too close. Dissipates when he is hit.
Use or Toss...I simply keep one in Rick's inventory for kicks, neither using nor recycling it...just because. Sometimes I play with it during the Twilight World Incident to liven up having to stand there fighting a single CIMA while the others get into position.
Equipment items used to block enemy attacks. They come in two types, the permanent status blockers and the one use shields. With only four slots for equipment you need to choose carefully between these and the Rings to get the type of characters you want.
Poison Block (ポイズン ブロック Poizun Burokku): Defends against Poison.
Use or Toss...As poison is hands down the most annoying of the status effects, I say use it. In fact, your first one can be found on the second floor of Beginning World, provided you ignore Jester's advice to close off the pathway at first and tackle a mid level CIMA. Not too hard a task to be protected for the entire game. Plus, the second is only found in Panic Factory, after the boss fight, making it an early acquisition as well.
Paralyze Block (パラライズ ブロック Pararaizu Burokku): Defends against Paralysis.
Use or Toss...Since paralyzing effects aren't too much of a pain, nothing Eberle or Jean can't take care of, it's more your call. My "Absolutely Necessary" setup for Ark consists of the Poison Block and two important Rings, so that leaves room for one more status defense. I personally don't bother with this one, since the other two statuses are more likely to affect me in a worse way.
Protect Block (ガード ブロック Gaado Burokku): Protects against defense weakening (I can't not make this description sound redundant). It's Japanese name is Guard Block.
Use or Toss...A toss up between this and the Power Block for me, mattering whether I'm worried about getting hit harder or doing less damage. I tend to stick with the latter after getting a Shield Ring, since most things that use status are not likely to beat the crud out of Ark, however I use this one until that time.
Power Block (パワー ブロック Pawaa Burokku): Protects against power weakening.
Use or Toss...Since doing more damage to kill things quickly is the best way to protect the pioneers as they walk past danger areas and you can't get a ring to increase attack power, I prefer to use this so I don't end up with less. My Ring based preparations deal with the loss of defense rather well, and I can survive paralyzed until Eberle is in a safe place to use her ability on me.
Status Shield (ステータス シールド Suteetasu Shiirudo): Prevents status effects one time, then it breaks.
Use or Toss...Used very situationally, in places the pioneers are exposed to poison but it will take time for me to get there. Normally I simply recycle the things, since Ark is filled up with equipment as-is and he's most likely to get hit.
Defense Shield (ディフェンス シールド Deifensu Shiirudo): Prevents an enemy attack one time, then it breaks.
Use or Toss...I definitely carry a few for rescuing Emmy, since the Dragon guarding her is over powered for the area you're in, Emmy has a combination of low defense and HP and even Ark can fall if you're not careful here. However, after that they lose their usefulness, since protecting your entire party with these on a regular basis would be an expensive prospect.
These are the stat boosting equipment pieces in the game. Mostly used for giving your characters a better chance at making it through the dungeon, I've been able to avoid tossing any and all of these things since even if Ark can't fit another in his inventory, someone can use the extra protection.
Speed Ring (スピード リング Supiido Ringu): Increases Speed.
Use or Toss...I don't use them for Ark, however the four I find I give to the H family one by one. Helps Halley and Emmy finish their broken bridge sections quicker, reducing the chance of being beaten within an inch of their young lives, and Eberle gets the third to keep up with her children and Jean the fourth for the same reason. If you're not moving that group, or when Jean/Halley is in the lead, you might wish to give a ring to a different character; I found no change in speed with my leader through Speed Rings or All Dash enhancements.
Shield Ring (シールド リング Shiirudo Ringu): Increases Defense.
Use or Toss...I give one to Ark to help keep him alive longer in boss battles and save some Majesties through making less potions. The second ends up on Emmy, since out of the characters with the lowest base defense she has the lowest HP and is put in danger more often when going across the bridges with her brother.
Heal Ring (ヒール リング Hiiru Ringu): Recovers HP periodically.
Use or Toss...The single greatest thing to ever grace my game file! Though the manual itself says only when standing, I've gotten HP recovery while walking around battlefields trying to avoid boss CIMA so I can set up my counterattack. You find a total of three in the game: one through Emmy treasure hunting in Dragon's Dungeon, one in a chest deep in Panic Factory and the last one after beating Zikjabel in Air Garden. Since the first two come in quite early, that'll keep Ark and Ivy in the clear as they wander around, and you can always pass them between wounded pioneers while the duo is getting the level set up for traveling, thus saving Majesties by not making and using potions. And it really helps your limited supply in boss battles, too.