As I get set to begin a complete restoration project on my '71 (it's literally in pieces), I'm wondering if getting an air compressor is one of those things I should get as I assemble all the tools I'm going to need.  If so, what psi at a minimum should I be looking for?

Every shop/garage should have an air compressor, imo.
That being said, how you use one should determine how big, and what type you need. If you plan on using any air tools, such as an impact wrench, you'll wanna get the largest capacity you can afford, with at least a 20 gallon tank. Air tools will drain a small compressor tank almost instantly, so get the largest you can. The larger the actual compressor, the better, with at least a 3hp motor.
If you're just planning on using air for airing up tires, or blowing dust and such, a smaller one will suffice.
My thoughts are to simply get the largest, most HP motored one you can afford...and have room for.
Adams' Apple2010-11-25 11:13:35

All air compressors including the small ones put out a high PSI. If comparing you want to look at the CFM cubic feet per minute @ (whatever PSI) say 90 PSI for example. They will all give you a CFM rating but a what PSI may vary. The higher CFM at a higher PSI is giving you more output. Also, as Joel says, the larger the tank the better also. If you can find one with a seperate motor and compressor head (belt drive) it is most likly a better unit. These motors have a slower RPM, but larger compressor pistons. Slower RPM = less noise and heat. The direct drive rigs at the big box stores run at a very high RPM, but have much smaller pistons.They are really loud which is a consideration if it is right there in the garage with you.

I have a snap on one that is never on sale..I agree with the guys above..the belt drive is what mine is and also a twin piston..the only thing that drains it is the cut off wheel..it does work the air hammer though..but it is so quiet that you can barely hear it run..a big deal in the garage..it is a small portable 15 gallon tank..I paid for it but it works beyond what I thought it could do..look for something twin piston low rpm..high cfm..small and quiet..quality air tools will also make a difference in how much air you need..cheap harbor freight air guns need more volume to do the same thing a quality air gun will do with much les cfm..that's why I get away with a small tank..I really have spent to much on that White truck in the parking lot every week..
Rich