I wouldn't honestly go for the "old classics" if you haven't played them before, as many people have a lot of nostalgia to help them enjoy those games despite their obviously aged mechanics. I guess some are still highly playable though, and if your into that kind of thing go for it!
Personally I think you should really check out games with good mod support, that's where PC gaming truly shines in my opinion. Games like Skyrim are constantly given new life due to mods, though if you already played it to death on a console I'm not so sure it would be worth buying again so soon.
Battlefield 2 actually has some great mods if you enjoy realistic shooters, with Project Reality being the absolute in realistic wargames as far as I am concerned.
Currently I'm playing and very much enjoying Planetside 2 Beta. Despite tons of bugs it's mostly a great time, especially if you can get some friends together. There is just something completely unique in the experience of charging down a hill towards an enemy fortification surrounded by hundreds of your allied players and vehicles, dropships thundering overhead. The basic mechanics are very simple standard shooter stuff, but in this kind of epic scale it's made wonderful...
Personal favorite RTS if Men of War: Assault Squad. My RTS-fan friends don't seem to like it at all though, so take this opinion with a spoon of salt!