Technically you can. I've seen 660s at BestBuy.
With a $300 budget, you'd be looking to spend about $50-70 on the PSU and about $200 on the graphics card.
For the PSU, I'd recommend the Seasonic G 550W because its Seasonic, modular, 80+ Gold and pretty cheap if you count the MIR:
http://www.newegg.com/Product/Produc...82E16817151119
Other recommended PSUs are in this list:
http://www.overclock.net/t/183810/fa...power-supplies . I would shoot for a cheap 500-600W unit on the recommended list.
For graphics cards in the $200 range, you'd be looking at the 7850, 660 and 7870:
http://pcpartpicker.com/parts/video-...82,110&sort=a5
This picture guide says: for GPUs ASUS, EVGA, MSI and Gigabyte are very good. Sapphire, XFX and Zotac are good. HIS is OK.