Question about compressors.

I tried to find answers to the following questions before posting, but didn't find anything directly on point, so here goes, and sorry if it has been addressed before.

My wife purchased me a Badger airbrush, along with some canned air. Now, I'm no rocket surgeon, but it doesn't take long to figure out that a compressor is cheaper in the long run. In looking at the prices of the small hobby compressors though, it seems that the ones you can find at Home Depot, Lowes, and places like that, are a bit bigger, have an airtank, are cheaper, and can be used for more things (inflating tires, balls, etc...). They are relatively portable, so I can carry them from basement to garage with no real problems. So the questions:

Is there a downside to them that I am not seeing?
What will I need to use one with my airbrush? So far, from looking at other posts, it looks like I will need an adapter to fit my airbrush and a moisture trap. What is the best place to purchase those items? I was at Home Depot last night, and the employee talking with me suggested Sears. Do they tend to carry those things, or should I look elsewhere?
Am I missing anything else?

Any and all help and insights are greatly appreciated.