Is there a particular format that resides over what sets are legal and whatnot? I've played casually, and I'm interested in tournament play, but is it "standard format" like magic where only the first few sets are legal?

It depends on what is scheduled for the week. If you go to www.wizkidsgames.com and register, you will be able to see if the event is restricted or not. There are some sets that have been retired which would not be legal in the restricted format. You can go to the following site to find out which sets are legal: http://www.wizkidsgames.com/wk_article.asp?cid=41760

Do the tournaments use marvel or DC exclusively, or does it not matter?

some of the tournaments have been dc only but thats because the new set crisis is having alot of events, i expect to see the new marvel set that comes out in july give us some marvel only.