DO NOT GET GHOSTS!!!!
The game runs like garbage, and looks like garbage as well.
It seems to hate AMD cards and SLI/Crossfire is buggy, and I get constant frame drops on my pc regardless of if I use 1 or 2 cards with or without my cpu being overclocked, and the lag is atrocious even tried it on a test connection which is far more than you can get now in a residential connection and it still lagged like crazy.
The support for the PC platform is none existent pretty much, and it is supposed to run on Dedicated Servers but it actually runs on a P2P connection so someone in the lobby, hosts the game and it always seems to pick the person with the lowest spec'd pc and slowest broadband connection, also there is only around 5000 players world wide now.
As for Resident Evil 6 I have not played it so I cannot comment on that.
I have tried various other FPS games but I cannot get on with any of them other than Titanfall, Battlefield 4 suffers massively from packet loss, bad hit reg and crashes and it's only Battlefield 4 and Ghost's that I have a issue with when trying to run them although Battlefield 4 is getting better.
If you are going to think about gaming then dependent on what resolution and detail settings you want to run the games, at you may need to upgrade your GPU and you will almost definitely have to upgrade your ram to 8Gb.
Look at some reviews of the games you are thinking about and see what people say about them, and then see if you can get them cheap so it's not a big impact if you don't like them.