If you need the compressor to operate a handpiece at home, you're better off buying it rather than renting as i think this would be cheaper for you.
You can buy one from walmart or sears ( check out their websites) and the price is between 100-200 dollars.
You dont need a compressor bigger than one horsepower. Dont buy a dental compressor those are very expensive and dont give you any real advantage over regular ones (except maybe for lower noise)