Originally Posted by Yorkston
Not sure why you would want to stay at such low resolution, but an old pentium isn't a very good choice these days. The optimum would be an i3 or FX-6300, but if you are on a really tight budget I would say grab a Richland APU. You can grab an A8-6600K, a cheap FM2 board, and 4GB DDR3 for under $200 an get pretty much a full system upgrade from what you have now.
The G2020 is an Ivy Bridge Chip, i dont think there's any Haswell ones out there yet and they run games surprisingly well for ~$65 mark CPU's, whereas the cheapest i3 costs nearly double, im talking about Australian prices here. Ok, Crysis 3 or Metro are probably a no-go on a pentium, but most other games do fine as long as there's a decent GPU in there.
For myself, i would definitely take an overclocked Core i5 in my primary system any day, however i've built low budget (~$500 and less) systems for others or for my own projects that could handle any game you threw at it at med-high detail with an entry level GPU. 1080p was fine in a lot of cases using the Pentium and a HD7750, you had to make an exception to play some games in 720p, but if the budget could stretch, performance would be a noticeably better, with a GTX650 Ti/OC and shouldn't bottleneck either and would still be fine if there was an entry level PSU in there.
Is OP reading all of this?