t260g's story is definitely a little different, and probably the most "normal" (compared to other rpgs. so maybe least normal for saga) because you can go around and do side stuff but you really, really don't have to and a lot of it is not as useful as it would be for other characters since you're probably using so many robots. instead just blowing through the game will hand out tons of loot and abilities for them so you can totally just follow the plot hooks for 100% of the game, and if anything the more stuff you try to do the harder the game gets by the end :/
since most fixed enemies in the game have pretty consistent stats in most regards and only gain health if anything. and in most cases this is hard to establish; the easiest enemy to observe this on is king sei, since you can see that deathsynthesis heals him more and more the later in the game you are. i have the impression this is true even of final bosses, but without going far into that...anyway, they don't really scale up the same way you might think, and are certainly not designed to be "in tune" with the dungeon enemies. unfortunately.
as a result it's pretty hard to finish any area with a boss fight very early in the game, which includes elements of both the arcane and rune quests. i would say the easiest areas to loot essentially all of and never "have to come back to" are wakatu (if you're doing the card quest) and the two shingrow ruins; the left one (spaceship) doesn't have a boss at all for the other six characters (as i recall), and the right one has a few miniboss type enemies which you probably can't do fresh out of intros but are easier than any other area boss i think and can give some hefty stat boosts. (it's also always worth going to for harmonium items and a sanctuary stone.) taking the treasures from sei's tomb is also a good choice-you can always put them back later to try to get a stronger sword once you're strong enough to beat him.
for blue in particular, you get to choose the next boss after you do the two magic quests, but in either case the boss is much harder than the preceding mandatory ones, so in any case if you aren't going to keep ng+ing the game to see the storylines you'll want to give yourself a quick jumpstart somewhere like the lab at the start once you have a set of characters you wanna use for a while (and the freedom to actually choose what you're doing, for some characters), and then maybe again even after you've finished some of the stuff you have to do. a similar rule holds up for most other characters i think.
since asellus can get one of the strongest swords in the game so early you can skip over some of that, but you can also become temporarily unable to enter certain areas until you can beat a boss, so that can be a bit tough. for riki though none of this really matters. you'll get randomly sucked into tanzer at some point very early and have to grind till you can beat the heart, and you don't get to fight sei for the sword, so there are almost no bosses after that until the end of the game. at which point they are all terribly difficult, but there's only so much you can do to mitigate that.
also, in remaster with ng+ i believe every character can pick up lute (and cotton, although as a monster he's somewhat more challenging to raise up to carry levels) unconditionally as soon as they can freely travel (to scrap and shrike), or alternatively fuse and gen by taking the card quest, so if you raise them up one time you can technically use that as your big bootstrap into the game
