Well we've only done closed beta so it's hard to really make a guide that is guaranteed to be applicable as the game gets updated and whatnot. But..
Bowmen:
shoots straight ahead, very similar to your typical shooting game character (think Marisa A in EoSD type deal). Owns bosses way faster than any other class given equal gear/level and whatnot. Was considered the worst pvp class however (I think, maybe magician too. Pretty sure it was bowman though). Oh...looks ugly as @%# >=P
Swordsman(even though they all female >=P):
Can't shoot, you have to melee enemies (your sword's range is not bad for a melee weapon, but still, you have to get close to your enemies). However, melee attacks also destroy bullets. Pretty good at soloing most levels, but quite possibly the absolute worst at soloing bosses. Interesting class that's fun, but definately not the class to play if you're hoping for your typical shooting game experience. Considered good at pvp, but not the best. When grouped up, often trivializes most bosses. I'm pretty sure people who are unconfident of their abilities will be wanting a swordsman in their group.
Magician:
Probably the best class when it comes to beating stages, not so best at bosses however (not bad either though I don't think). Pretty much decent at everything I believe. My brother rolled this class, and it really looked interesting. Probably the class to pick if you enjoy shooting games with weird/innovative weaponary (like hellsinker).
Summoner:
Reimu (homing amulet type)pretty much. I mean, homing attacks, piss poor dps, and I believe has a strong ultimate attack (though I've never seen it myself, it's just what I heard). I always hear they are god at pvp, again, never seen them in action though. I believe this is considered the best class at soloing most content, bowmen is better at bosses, and magician I think is better at trash, but summoner is good at both. Not as useful at the abyssal labyrinth however from what I hear due to poor dps combined with lack of utility. But again, I have no clue. I haven't really seen these anywhere ever except wandering around town and being in parties that are not my own.
I personally played a bowman, and if you can beat Touhou games on hard (or lunatic), you'll probably be able to solo anything and everything as one, including the abyssal labyrinth. I was able to without much difficulty, but I only hit level 30 something, so I wasn't able to try the higher difficulty labyrinth stages, only the ashy key one.
