*Links/pricing are United States. They're just for reference.
1) As mentioned, your Power Supply must be compatible.
You can mostly just look at the available 6/8-pin connectors. An HD7770 for example requires a 1x6-pin connection but a GTX770 (much better card) requires a 1x6-pin AND a 1x8-pin.
2) Your CPU will bottleneck the really good cards but it VARIES a lot per game. Basically just get the BEST card you can afford.
3) What card?
I recommend spending between $110 and $330, but your budget and choice of games will determine things.