I'd wait for a summer sale. There should be one fairly soon. You can pick up a good deal of highly discounted games. I'd without a doubt recommend XCOM: Enemy Unknown and the accompanying DLC that comes with it. I believe it also came out on android, but I'm not sure if the saves would sync up. XCOM being your nice run of the mill, but highly polished, turned based strategy.
Greed Corp is a good turn based game as well. A bit more difficult I'd say, but the strategy element is there in force.
Metro 2033 and Last Light are both excellent games that will push your system to it's limits if you don't have a top of the line gaming PC. FPS with heavy stealth and horror elements. Excellent story on both games. Last Light is a bit easier to play, and won't make your system cringe.
Half-Life 2 and the other episodes are worth playing. It's an old game now, but it still holds its own.
Oh, and if you have the friends and time. Borderlands series of games is worth looking into.
FTL is a fun game to look into. It's quite difficult, and unfair, but it's incredibly addicting. Same for Risk or Rain. Both are rogue like I suppose, and both are damn fun to play over a few short minutes, or hours. Your choice.
I'd also avoid RAGE and The Bureau. Both games built up an amazing amount of hype, and fell short. In RAGE's case it fell short catastrophically.