I think Seamaiden and Bulldog covered the basics pretty well. Take a look at that chart, think about what your main goals for the cover crop is then select what plants will work best to achieve that.
The one thing I would add is that cover crops also make for great weed suppression with the right mix. In my opinion that is actually one of the biggest benefits we have seen on our farm, not having to pull weeds is a huge time saver, especially ridiculously gigantic weeds that have been supercharged by our nice rich soil. Once established cover crops can be more effective than herbicides in my opinion.
Using a mix of plants is generally considered a good way to improve the bio-diveristy of your soil and preserve it's health as well. Our mix always has a blend of severa species. This year was Fava beans, Bio-master Peas, Yellow Peas, Sugar Snap peas, Purple Vetch, Common Vetch, Hairy Vetch and Cayuse. The main goal for this mix was weed suppression, improvement of soil organic matter, and to create a habitat for beneficial organisms. The sugar snap and yellow were a new addition, and we added in extra peas and fava beans in the hope that maybe we could get some food off the cover crop this year as well (I love fava beans!).
Oh and birds love cover crops. Consider bird netting if it becomes a big issue. I just seed at 3x the recommended rate and figure the wild life will get half of it.
