Sorry, in my haste this morning I left out quite a bit of information,
My current system is
Intel pentium G860
4gb DDR3 1333
160gb Western Digital 7200
I play a wide variety of games, I can run most of them no problem, I start having trouble when trying to record gameplay, I use a program called Bandicam which seems to be a lot better than fraps when it comes to system usage. I always record and play in 1280x720
Since you record at the same time, and play at a relatively low resolution, a CPU upgrade may do more for you than a graphics upgrade. A HD6770 shouldn't be having any difficulty at that resolution.
Take a look at this: http://www.tomshardware.com/reviews/gaming-graphics-car... and note that Don recommends a three tier jump. Personally, I think two tiers is likely to be visible, but that probably means maxing your budget, at least to get a HD6870. Then there's your PSU; is it up to the job of powering a much stronger card?
Edit: My guess is, no it isn't. The little voltage switch gives it away as, at best, an inefficient, overrated older design. I wouldn't try to get any more than 400W out of it, max. A quality modern PSU has full range active PFC (no little voltage switch), and some level of 80+ certification. Seasonic, Antec (their VP-450 is an exception that proves the previous rule), Corsair, XFX, or Enermax/LEPA are among the better brands.
I think jtt283 gave you a much better/detailed answer. I was also trying to find info on your psu - like jt283 said - any psu that cannot automatically adjust to voltages from 110-240 vac is an old design at best. Likely inefficient, poor power factor correction and not very good build quality.