Well, about compatibility there are two factors as far as I'm concerned for graphics cards:
1. Graphics Card Slot:
There are mainly two variants for this: One is
AGP, and the other is
PCIE 16 (Note that you are looking for PCI
16 as the graph in the wiki page will show) Just take your Motherboard's box, manual, or anything like that, and look for the the name of the one you have. Or if you have none of those you could always open your computer, and see for yourself.
All this being said though...unless your computer pre-dates something like 2005-6, it's very unlike y you have AGP as it's a very old model which has pretty much already died out.
2.
PSU Power Supply
This is a box which is typically located on the back-top of your computer case. You can easily identify it as the box where you plug your computer's main power into.
PSU's are most generally measured in power by their
watts (W), and although there are other factors this is mostly the most important one to look out for especially if you're a newbie. The watt number is typically on stickers on the side of the PSU.
The higher tier the graphics card, the better power supply you'll need to support it. For instance some mid-tier graphics cards can run nicely on 400w-500w while bigger ones may need up to 650w at least to be safe. It all depends on the card, and you should look out for the minimum requirement before purchasing.
EDIT: Oh and the GeForce GTX 660 Ti is a fairly powerful card (Even better than mine lol), and it'll serve you well for gaming as long as you're not into insane stuff. 650 is quite awesome too. You can run Amnesia on max no problem with either of them.