Beanie and Mendenhall are both guys I'd really look at. Both should cost very little money and have a few things going for them.
I really think running backs tend to hit their stride around 24-27. Those are the absolute best years. The guys who work harder last even longer.
Beanie has played his entire career behind a pretty bad offensive line. The only problem with him is the potential injury risk, but that injury risk is one of the main reasons we can get him cheap.
Same with Mendenhall. Similar age, good experience now, should be pretty cheap. Has been successful in the past.
Both of these guys I would take chances on over Shonn Greene.