We use eye round, which is lean and easy to slice by hand with a sharp knife. You can get it pretty cheap at places like Costco, around $3/pound.
If you aren't willing to slice and are willing to pay more, you can often find thinly sliced beef in an Asian market.
Without a dehydrator or an oven with a fan, I'm not sure what the best method would be. Perhaps the sun? :-)
EDIT: We use a Nesco FD-80 American Harvest Square-Shaped Dehydrator. Super easy to use and clean.