Help me pick a GFX card/upgrade my PC

I have a Dell XPS 7100 (2010) that is starting to show its age. I bought a whole bunch of games during the Steam summer sale that I cannot play, and I would like to mend this. Most of my problems have been in terms of frame rate at 1600x900. I don't mind playing with low texture quality, etc. but it would be nice.

Full specs of rig as is:

I know very little about PC parts or upgrading, but from my understanding the biggest things that would constrict my decision would be case size and power supply.

I'm basically wondering: what would be a good GFX card that would work with my rig as is? Would it be worthwhile to upgrade my power supply as well? Should I be scrapping my rig and building a new one altogether?