New computer means new games, but I need some help.

So I just went from having a shit laptop to a pretty nice one. It's no gaming computer, but it's a start. I want to get a few games for it, but because I've never been much of a gamer, and having a shit laptop for so long I've fallen out of the loop. I need your guys' help in recommending me some good games for beginners.

For specs, I'm not sure what information is relevant, but I have 8 gigs of ram, running windows 7 64-bit, and 750 gigs on the hard drive.

As far as games I like, I love the hell out of minecraft. I love the simplicity and openness of the game. The multiplayer factor is a big plus for that.

On the console I play tons of skyrim, and once again it is the openness and the ability to do whatever you choose that is what draws me to it.

Outside of those two, the most contemporary game I really got into was Spyro for PS1. So yeah, I'm behind the times here. Please help.