I have used my small home compressor with just fine results. Trick is to have a large enough tank, the compressor is not really the issues.
You want a tank that can hold enough volume that you do not have a drop in pressure while sanding as that will slow the sander down. If you go with a small tank then you should just keep an eye on the pressure in the tank and down work when it is below the optimal pressure of the tank and wait for the pump to re-fill the tank.
Mine is a 6.3gal tank with an electric pump putting out 1hp.
If you do use it often go for a unit where you can service it (change the oil) as it will extend the life of the compressor. Mine is a sealed unit so it's not made for lots of use.