Low end entry level rental cars are generally around $15 to $30 per day ... it depends on location, and whatever discounts you are able to get, and possibly when you get it.
You might be able to get a better deal for a longer rental period.
Lease usually requires a huge down payment, you probably wouldn't get that back.
You might want to consider buying an old used beater car ... like a late 80s Honda or Toyota or something ... and then resell it after you are done with it.
Assuming you get a halfway decent deal on the thing (buying from a private party), I don't know how much on average you would lose, and I don't know if this is really a "viable" option, but, it might be worth investigating.
<--- EDIT ... ok ... Mattlocs idea is the same thing I'm trying to convey here, but he said it much better ... hehehe