@Kariva An Nvidia 770 would definitely do fine, although I'd still check your power supply to make sure it supports the card. A 770 can draw up to 230W of power at full workload, and the recommendation is 600W, although you can get away with less. If you do start to have trouble with it, please post back listing the specs of your PSU.
@Kariva The symptoms would be difficult to miss: graphics glitches you can see on your screen, game crashes for no apparent reason, even shutdowns or restarts of the system. If you don't see anything like that, I wouldn't worry too much. Still, it would be a good idea to have someone who knows what to look for run a couple of monitoring apps at some point, just to make sure the computer is running as expected. It's not urgent though.
