Alfalfa is great, any legume will do. I'm using a commercial mix, but I'm covering acres and improving sandy clay loam soil at the same time - my mix is mostly clover, plus winter/field peas, hairy vetch, daikon, common radish, some mustards and some grains. Its very forgiving of soil variations, due to the variety - which isn't something you need to concern yourself with, but is of major importance to me. The chickens seem to enjoy it, so will the goats when I finally have some.
$10 will get you a 1/2lb at Amazon, $15 will get a full pound of a similar mix. I buy in 50# bags at a MUCH better price point per pound - those prices are like trying to plant commercially with those seed packets from the big box stores.
Locally, most of the farmers use rapeseed in their cotton fields, which is a brassica (a "mustard") - that would work for you too, just make sure you till it in before it goes to seed.
and of course, Alfalfa is spectacular.
Basically, whatever you can get that's cheap. Even annual winter rye, if you are desperate and there are no alternatives.