Thanks all!
What games do I enjoy? Well, I've recently (going on a year now) fallen away from videogaming and really got into boardgames (specifically, those known as Euros). Strategic videogames that are similar to boardgames appeal to me. Right now I've been playing, learning, and getting demolished in Civ IV: BTS (chietain difficulty) as I try to figure out the strategies. Another game I enjoyed but eminently gave up on was Patrician III, mainly because there was too much going on under the hood and the fact that I couldn't see what was going on bothered me. Civ IV, while it has an overwhelming amount of info, most of it is available to read.
Sometimes to let off steam I'll play TF2, though if I somehow never played it again I wouldn't miss it. I also just started playing Metro 2033 last night, a game I bought ages ago that I never played. But ignore those, AAA games for the most part don't interest me (except I'm a sucker for Spider-man games, and want the new movie tie-in one).
Most of the games I bought here a while ago when they were on sale or free.
Sanitarium, since it's short, sounds like a good first game. I bought it because it was on sale and looked charmingly appealing. I've heard a lot of good things about Stronghold and I really like the fact that it has a campaign, which allows you to learn the mechanics incrementally (Civ IV needs a campaign like no game I've ever seen).
HoMM3 I've heard similar to what many here have said. I'm going to save that for last if it's so long.
Populous 2 I feel I need to play as I've heard great things.
The funny thing about being a boardgamer is that these old games are more appealing due to their reliance on numbers and engine building.