As far as carry-over stuff, all you have to do is have an epilogue save in XS2. (And all you get out of it in XS3 is a graphic-changing piece of armor for Shion - her Vector uniform - the stats of which you'll eventually upgrade past.) You don't have to do all the optional stuff, none of that has any carry-over effect. Although doing the Dark Professor sidequest does make the relevant sidequest in XS3 make a bit more sense. And the third optional side area (Heavenly Ruins or somesuch) is also rather pretty imho.
My advice on XS2, which is almost exactly opposite of my advice for games in general, is this: Haul out the Codebreaker (or whatever) and cheat your way through it. The game's battle system has a great deal of lovely potential but it falls short on execution in a number of ways, to the point where certain cheats (like infinite skill points) give you interesting tricks to allow you to actually appreciate the battle system *more*.
Otherwise it's just a yawn-fest of stockstockstock, boostboostboost, cast sword ethers, cast attacker/ether spear ethers, unleash massive combo of destruction, win. With a bit of healing thrown in now and then. Random battles are, regrettably, pretty much the same except you can generally stick to just the stocking and boosting and not fuss with the ethers. (But the random battles are consequently pretty damn slow, and they get slower as the game goes on.)
Be careful about making yourself too powerful though, you do *not* want to be one-shotting the final-final boss because that battle isn't technically won by reducing his HP to zero, and you'll need to hit him with attacks that *don't* kill him, to win. Infinite skill points, infinite EP (this one's particularly broken once you get Erde Kaiser Fury: you can finally make random battles in this game be *fast* like in the other two), and massive exp gain so you promptly hit level 99, should be more than enough. Don't go maxing out your stats to levels you'd never legitimately be able to reach though, that'll kinda screw you over.