inspiron 660 full tower psu & gpu upgrade

Solution
If this is the inside of your PC, any PCIe x16 card should work. http://i42.tinypic.com/2144k5i.jpg
That's a mid-tower, not a full tower, btw.

And any ATX PSU should work as well. So yes, the GTX 970 and Corsair PSU should be fine.
The i3-3220 might bottleneck the GTX 970 occasionally in CPU limited games, but overall, not a deal breaker.