I'm not sure what you could really get for that price with GPU included that would do anything halfway decent.
With what you've got now, you'd need to replace the Mobo and RAM at a minimum.
If you could pick up an i3 Haswell, that might get you what you want with the integrated graphics. Anything older would be too slow to be of much benefit.
Ultimately, if I was doing a complete system upgrade on a budget, I'd shoot for a Pentium G4560, 8 GB RAM, and cheap motherboard. Then you can save up for a GPU later and have a pretty decent gaming system, but the G4560's iGPU should handle those games at playable framerates.