Tomb Raider

The Angel of Darkness is the WORST TR game of them all, don't even bother playing that one. Play them all (except AoD) - even the original DOS games, which all will work just fine under Windows XP.

You don't need to play the Tomb Raider games in any sort of order. It's not a particularly story-driven game series, there's not much of a background, or any sort of plot running through the series or anything.

The games each have their own contained stories, which are just there to make the game seem more coherent and give them some direction, they're not particularly good stories or anything. All you need to know is that there's this posh girl called Lara Croft, who travels the world looking for ancient artifacts.

So no, you're not missing out by starting from Angel of Darkness. Tomb Raider and Tomb Raider II are the best games in the series though, be sure to play them at some point.

You don't have to go that far back. Tomb Raider Anniversary was pretty much an updated version of the original. I would say to start there and then go to TR Legends and then TR Underworld ( the order you play them really doesn't matter much). I've played all these and they are alot of fun. The only complaint I can think of would be the way you have to pull off a special move in boss battles in Anniversary. I hated that to the point I almost quit playing it (I used keyboard controls).