I've run my 7850 with these settings on cgminer 3.1.0, 3.2.2 and 3.7.2:

-I 17 --thread-concurrency 20480 -w 256 -g 1
or
-I 13 --thread-concurrency 8192 -w 256 -g 2

Either are ok for me. I get around 300kh/s at GPU clock 860, memory clock 1150. People who are willing to overclock can get better results. I don't like how some things are displayed on 3.7.2 though.

Change the intensity (the -I #number) depending on how far your card can go and how unresponsive a PC yourself can put up with. 4GB RAM is enough, that shouldn't be the problem IMO. If you're running one or two 7850 card, that shouldn't be demanding on the PSU either.

Edit: In cgminer, A means accepted shares count, R means rejected count, and HW is the number of hardware errors. Your screenshot does show a lot of HW's.