Do the different characters effect the game at all, or is it just for aesthetic purposes?
Yes, they affect both the pieces you get, and in the Fever games/15th Anniversary, some characters have stronger Fevers than others. The drop pattern is shown when selecting a character in 7 now. All characters' drop patterns differ except for Arle Nadja, who will always drop the classic Puyo Puyo 2-piece I.
Feli, for example, has the following pattern: L (right solo), I, O, I, L (top solo), I, H, I, O, I, L (right solo), I, H, I, L (top solo), I, then it repeats, for a total of 44 puyo dropped over a 16-step period. Higher drop numbers are generally better as long as you know what to do with them, making Arle actually one of the hardest characters to play as she will generally drop only 32 puyo over the 16-step period.
One of the reasons I like to use her is that she is the only character to start by dropping an L-piece, and as long as I can clear one of the two colors of it with my I, I have a guaranteed and very quick All Clear, which sets up an immediate 4-chain for me to either fire off or build upon. It's a devastating strategy if done right off the bat as it immediately gives your opponent several rows of garbage, but the risk you take with that is that they can fever/henshin much more quickly.
@ Hasuko
...Wah. Now I really want it. I'm a sucker for artbooks. A very big sucker. (I just downloaded about 100 of them off a private tracker I'm a member of...)
You got some taste, too. GITS SAC 2nd Gig, Ar Tonelico, Puzzle Quest... hell, even Eternal Champions for the Genesis. If I weren't already taken, I'd be positively smitten, lol. I'd better not show her that stuff, she'd drool over some of it too. Especially the loli. She likes them quite a bit.
I can get you into that tracker if you're interested though, just drop me a PM. If it means I get an artbook or two out of it, an invite to it is a very easy thing to give up.