I think your approach is good. There isn't a lack of projects to contribute to.
If you are interested in gaming, you are more than welcome to send pull requests on the various mogade systems:
Since you seem more interested in web stuff, mogade-server is probably where you'd have the most fun. mogade.com is already live and has some live games. Its also closed source. This is the v2 engine which I decided to open source...hopeful to go live this month.