The thing about an impact is, the CFM ratings they give are for constant use - i.e. holding down the trigger for long (relatively) long periods of time.
That's not typically how most impacts are operated - they're operated in short bursts for all but the most stubborn of fasteners.
As such, while a particular gun may call for a 5 CFM supply, a compressor with a 3 CFM rating will typically perform just fine (my own personal experience with my very first 5-gallon cheapo compressor).
Continuous-flow style tools (such as a sander or a cut-off tool) are FAR more strict about their supply needs. On one of these style tools, and a small tank, you're going to frequently be pausing, waiting for tank refill, then resuming work.
In most cases, you're going to want to consider the CFM rating @ 90 PSI. As an example, this compressor from HD:
http://www.homedepot.com/p/Husky-60-Gal-Stationary-Electric-Air-Compressor-C602H/205389936
Has a rating of 11.5 CFM @ 90psi.
This would likely fulfill most "DIY" needs, but, as always, bigger (i.e. tank, motor HP and pump) is better.
I have two compressors:
Craftsman (Devilbiss) 33-gallon oil-free, rated at 1.7HP and ~5 CFM @ 90psi. This works for most of what I do (impact gun, ratchet, limited cut-off/sanding, etc.)
Campbell-Hausfeld 80-gallon oiled, 7.5HP motor, 2-stage pump, rated at 27.2 CFM @ 90psi. I bought this to plumb my whole shop, which I still haven't gotten around to. I've used it a couple times for some extended sanding work, and the thing is unstoppable. I bought it used for $650, delivered, which I believe was a HELL of a deal, considering the current model sells new for ~$2000.
Used deals are out there, but it just depends on how much you want to spend, and how long you're willing to wait for the "perfect for you" compressor.
I can't say anything truly negative about the 30/33 gallon Craftsman units, and the comparable size units that HF sells get good reviews on this forum (with the vast majority of negative reviews being from the anti-HF crowd with no direct experience with the item in question).
The best research you can do is look at specs of a compressor you're considering for it's CFM/SCFM rating @ 90psi, and then compare that to the supply requirements of a specific air tool that you're considering.
Most 30+ gallon compressors are going to be rated for 150-165psi or more, so supplying a constant 90psi or more is a non-issue.
