Mutation is probably the most trouble free one of these since you can "get away with" the 51-54 armor set on everyone without problems, as Mutation armor is elementally balanced (other than the 36-38 Dark set).
Infection (and Outbreak) armor, you have to be more careful with because, other than the extreme newbie sets (levels below 10) all the armor from these games is elementally biased. Loading up on a single element's armor (which you do, if you use the cookie cutter Thunder set in Infection) is normally a BAD idea, for two particular reasons. The first is that you will have a very limited variety of skills, you'll only be able to cast spells of one element which makes it much harder to get Elemental Hits (and if you get an enemy of that element which is also Physical Tolerant, you'll be killing it really slowly indeed ...). The second is that you'll be extremely weak to enemies of the opposite element.
You might think that being able to cast super powered Wood spells, say, by having the whole Wood set against Mu Guardians is cool, but Mu Guardians often appear in 2 or 3, or come with Goil Menhirs that must be taken out first before you can keep other enemies dead, and you'll quickly learn what it means to suffer sand erosion ...
Level 51-54 armor isn't so bad, though - however, do watch out about Medium Gloves in Mutation (any of the four from the sets from levels 36-54) - unlike the medium gloves from the other games, these ones LOWER your physical accuracy and evasion. Characters like Kite can get by just fine with these with their insane natural accuracy, but characters like BlackRose or Piros should probably stick to heavy gloves, with their single hard hitting attacks for which a miss can be a real problem.
Note that level 52 and 54 armor can be a bit hard to obtain in bulk; 51 seems to be max for Springs in Mutation, and I'm a bit fuzzy on locations for the 52 and 54 pieces. I do have the following knowledge -
* Both the Osorezan Socks (52) and Magic Leg Mail (54) are in the Gott Statue in Lambda Chosen Solitary White Devil. (BTW, these keywords in any game from Mutation onward give a high level area for their server with a B2 dungeon and no portals on the Gott path - just go East on both levels. Even in Infection, there is only a single portal per trip in the middle of B2)
* Segmentart (52, body armor) can be Data Drained from Brown Wyrms (Earth element dragon found in level 50 areas). Armor of Hell (54) cannot be Data Drained for; it must be traded (there's a couple copies available) or found in a Gott Statue, I don't have any specific keywords though.
* Neither the Demon's Cap (52) nor Devil Helm (54) can be Data Drained for, so these too must be traded or found in the Gott. But they are not worth using; in Mutation, you want everyone to have Light helms in order to be able to use Ola Repth and Rip Maen, as a LOT of damage starts getting thrown around later in the game. Any Light helm will do. The small loss to Physical Accuracy and Evade - Imp Earrings (51) have the worst loss, and that only -5 - is well worth the security of having all party members able to all-heal. Imp Earrings can be found in Lambda Chosen Solitary White Devil's Gott Statue.
* Cursed Hands (54) can be Data Drained from Sphinx Menhirs. You likely will obtain some, as one of the story dungeons has them and very often you HAVE to data drain them (as it's really the only efficient way to take out multiple Menhirs in one battle). Drain Gloves (52) cannot be Data Drained for, but the Geist Ring (51) is probably a better choice on balance (the magic stats are slightly worse, but both gloves carry Skill Drain, the Geist Ring has slightly better skills and punishes your PAcc and PEva a LOT less - only -5 compared to -13 for the Drain Gloves) and can be upgraded to via the Springs of Myst.
For weapons, it's somewhat more difficult to come up with a real 'best' choice, but here's my thoughts -
* Twin Blade - This depends on Kite's build (I don't use Natsume or Moonstone much outside their quests, so I just give them whatever I can get that's half decent without putting a huge amount of thought into it):
Full-on Physical Kite: Bloody Blades (give Critical Hit and 3 different elemental attacks, and the second best physical stats in the game - only the postgame bonus weapon is better, but only by 1, and its skills aren't as good). Get these from the Gott Statue in Lambda Chosen Solitary White Devil. They give no elemental stats at all.
Full-on Magic Kite: Yosetu & Fuyou (gives a basic physical attack just in case, plus the spells Vak Rom and Rue Rom, the latter being especially useful as Twin Blades don't normally have access to Water skills). This is easily traded for early on. They give +5 to all elements, which is the best on a non-rare Twin Blade until Quarantine. The Fishskin (DD Squidbod, rare) is also a good choice, with the best magic stats in Mutation but only giving a bonus to Wood, and having a Water spell too but not a Fire one like Yosetu does.
The Blades of Bond are also good, but a tad overrated; their only real claim to fame is having the best Element stats of any Twin Blade in Mutation, and really of any Twin Blade entirely other than one of the LV 99 blades in Quarantine.
* Heavy Blade - You must bring BlackRose so many places (and I personally used Sanjuro as my third most of the time this playthrough of Mutation) that this is worth discussing in detail as well. Personally, three blades come to mind here, the Sharktooth (I got mine through upgrading a Stonecrusher three times), the Laevateinn, and the Ghostdancer.
The Laevateinn has the best attack of any heavy blade in the game and also has Critical Hit; however, House Golems are an extremely irritating enemy, with 5000+ HP, nigh-irrevocable Physical Tolerance (seriously, I tried Dek Vorv several times with no effect - even if it did, you have to use magic to Protect Break them, and getting the Laevateinn means Data Draining them) and using Ol Repth frequently at low HP. If you do get one of these blades (though you won't encounter House Golem till either late in Magus' dungeon or in the bonus dungeon of Mutation unless you go out of your way to get one earlier), it's probably the best choice for a Heavy Blade, with the only real competition being the Ghostdancer.
The Ghostdancer is only slightly less powerful than the Laevateinn (24 vs. 26 PAtk); it lacks Critical Hit, but does give a useful +5 to all elements; as the most powerful attacks you'll suffer are elemental this is a good thing. If you use the Blades of Bond on Kite, you're probably of the sort of style who would use this.
The Sharktooth is the highest level regular Heavy Blade that carries Critical Hit; this ability is especially useful as a lot of enemies (such as Phases and King Worms) have no weakness in this game.
The Spark Sword is bad; Dalaigon Anecdote becomes far too strong.
* Wavemaster - The Data Drainable rare wands Jester's Wand and Dark History from INFECTION are still the best in Mutation as well, unless you really need a specific elemental attack. Jester's Wand in fact has the highest MAtk of any wand in the entire series (even the Banyuinryoku in Quarantine has only +24 vs. its +25), while Dark History's +22 is quite close and comes with a nice +25 MAcc too. Keep these wands until Quarantine (when stats get close to them, and the higher level skills thus become more attractive).
* Heavy Axe - Piros can take whatever, other than that if you plan to use him against Magus, I would not use the Key Axe; Magus' most dangerous attack is Wood Element. I do try to keep Piros' equipment current but I don't normally use him much outside of his required areas, so I don't pay too much attention to the weapon other than elemental weaknesses.
* Long Arm - Meh, whatever. Mage Spear is probably best, as the two rare weapons are hugely elemental unbalanced.
* Blademaster - Precious little differences; Menhir Sword gives +5 all elements, while the 6 Side Blade, 7 Star Sword, and Lion's Blade all give balanced element bonuses too. Don't bring the Matoi if you use a Blademaster against Magus, that's about the only caveat. I like the 6 Side Blade myself, mainly because I find it pretty easy to get (DD a Temple Knight).