I'm not a GM, so I have no idea how to run a game. But I remember being a player was a lot of fun, and I really want to do it again.
GURPS is the "Generic Universal Role Playing System". (
http://en.wikipedia.org/wiki/Gurps) It's an RPG system similar to DnD, for example, but generic so that it can be used in pretty much any setting (futuristic, modern, fantasy, superhero, whatever).
As for the kind of scenario that sounds cool to me, I'm a fan of the slightly futuristic, dystopian, noir, kind of setting.
Play-by-post is like it sounds. Instead of players verbally describing their actions, the do so via forum post. There are various tools to help with this (I guess) like dice rollers etc. I'm not really experienced though; I'm hoping someone here is a bona fide GM.