Too bad you don't want fighting or racing games. Those are the best.
For PC, you should DL Streets of Rage 1, 2 and 3 but it doesn't seem to be what you are looking for. It's a beat 'em up series, one of the greatest video game series ever.
Being a gamer is awesome. If you really want to be a gamer, try a bunch of different games. Don't narrow it down to only a few genres of games. Keep an open mind and play games you wouldn't usually play. You will find that you will enjoy a lot of games you never thought you would.
A lot of people like to stay away from certain genres because of stereotypes or they just plain don't like those types of games but you really need to knock down that barrier and play as many different games as you can.
A great, fun puzzle game is the Puzzle Fighter series (the girl in my avatar is from one of the games).