With limited money and parts, what would you recommend

Alright so my girlfriend is looking to upgrade her computer. Right now she has one still running an AGP card lol. It's time to move up.

She wants to play games but obviously not anything with ridiculous settings but at least medium. Her monitor also only supports 720p so no need for crazy resolutions. We have the case, PSU, and other little things like an optical drive and hard drive.

So the limit is $300 and that's max. I see the AMD A10 5800k but it looks like it can't really run games all that great. But at the same time, all the benchmarks I see are 1080p.

So basically we need RAM, Mobo, Cpu, and Gfx. I know it's a lot for limited money but there's got to be some kind of config that'll do this.

http://pcpartpicker.com/p/Jj76

Best I could do for $300. What power supply do you have?

I dont remember the PSU but I know it's atleast 450w. The way I'm looking at it now is the A10 can play games alright at 720p and later on down the line she could upgrade the GFX card and get better performance. No? Also Asrock Mobo, A10, and 2133mhz RAM would come out to like $250.

I upgraded his build to this. It costs $291.95:

http://pcpartpicker.com/p/JjvH:

I made another build including the A10 like you wanted that included a GPU. The reason for that specific GPU is that you can run a crossfire with the APU making the performance a lot better. I kept 1600 Mhz RAM but made it into 2 sticks of RAM because having only 1 stick will slow down you computer. This one costs $282.95

http://pcpartpicker.com/p/Jjzh