The included PSU will not handle anything stronger than a HD7750, which is fairly close to your $100 budget (especially after tax and/or shipping).
That will provide a system able to play games on low to medium (at best) settings (@1080p; you'll do much better at 1366x768). The newest games may not be enjoyable. Older games should play somewhat better.
Personally, if you want to play games, I would not spend any more than that on this system. If a larger budget later is a possibility, you might do better selling this one ($75, to use as a web-surfer) and putting the money toward a new rig. If that isn't possible, the HD7750 should still allow you to enjoy a lot of cheap games on Steam, anything Flash-based, and older titles.