Will my video card upgrade work fine?

So you are upgrading the the GTX 650? I believe that will work, though if you are willing to spend just a little bit more you could get the GTX 750 or 750 Ti, that have a Maxwell architecture which will be more powerful and more efficient.
 
Don't buy that PSU, not reliable at all. If you're looking for a super-budget PSU this would probably be your best choice:

Power Supply: EVGA 400W ATX Power Supply ($25.98 @ Newegg)
Total: $25.98
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-12-08 14:47 EST-0500

Also Cityfans135 is correct, the amount of performance gained from the 640 to 650 is negligible. A solid GPU upgrade would be to a 750ti, and the PSU I recommended above would power it perfectly.

Video Card: EVGA GeForce GTX 750 Ti 2GB Superclocked Video Card ($123.99 @ NCIX US)
Total: $123.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-12-08 14:49 EST-0500
 
The problem is the video card is free because my cousin gave it to me. I've had the GTX 650 before and it ran Heroes of the Storm on lowest graphics with no problem 60+ FPS. The GT 640 I have can't get 30 fps on Heroes of the Storm on the lowest settings while going into the ini files and removing a bunch of shit to help performance. Also I can wait to return the power supply up to late January if I have any issues, I just wanted to know if the GTX 650 would run fine with my motherboard & RAM.