Phx arizona alternative Lawn

My current lawn is ... well not really a lawn.

Its mostly dirt with some grass and more weeds. (not that i care about the weeds)

I was thinking of doing a clover yard, then i got to thinking about it why not just make it some mix of stuff.

different types of clovers, but what else would go?

I read somewhere that alfalfa can grow with clover. I think a good mix of covers would be better then just one. Also if its edible the better, I have pigs also (though not in the part of the yard)

Should I till my yard up I think the soil is pretty compacted, or should i just seed inoculate it and cover it with straw?