The first date can be very awkward. It should be kept simple, just a chance to see one another and make sure there's a physical connection without too much pressure. The second date should be more fun though!
It depends on the person it's with. I just want both of us comfortable so we can talk.. Could be dinner, coffee, bar or a trip somewhere. Lose track of everything so interested in each other and want to know more.
I think a casual lunch would be good -- we should both be as relaxed as possible, which is often hard for a first date. I am a pretty casual person; I can dress up, but would like to be comfortable for a first date.