I am interested in purchasing an air compressor to help me with projects around the house. Specifically, I want to have an air compressor that I can use with a finish nailer and to use for small spray painting projects (like painting furniture or my deck). What size air compressor would I need to be able to do both functions??

A finish nailer or a small paint sprayer doesn't need much - you can get by with a small pancake compressor like this:

http://www.lowes.com/pd_253750..._dollar|1&facetInfo=

In compressors, bigger is always better until you get to the point that they are hard to move around. Every air tool will have a rating for air volume, compare that to the compressors output, add a little more and you'll have what you need.

Most people have no idea what CFM even means.
Cubic feet per min.
Most people just look at the PSI rating.
CFM is way more important the PSI.
One way to think of is if you had just 1/4 plumbing in your home and you but a gauge on a faucet it would read the same as what ever your pump or city water was set at. The instant you open the faucet the pressure will drop to 0 and there will be bearly any flow.
For spray painting I would suggest using an HVLP or an airless sprayer.
If you do not already have nail guns it's cheaper to buy the compressor and guns as a set.
Check out CPO tools for some deals. They also have factory reconditioned tools with the same warrenty as a new tool and are much cheaper.
Look for a set with a finish nailer and at least a framing nailer.
A brad nailer is all but useless unless your doing tiny work.