Welcome! There is a post on air compressors. I'd link it for you, but I'm just too lazy to search at the moment. Short of it: You could get by with a smaller one - if you like to wait for it to build up pressure. If you're into waiting, get a larger unit. If you do, I think you'll be glad you did.

The thing about pneumatic tools is that they are generally really cheap, and also smaller and lighter than electric units. It's also really easy to switch them out. Not that a cord is hard, it's just not quite as convenient.

Air tools I've bought, used, and found useful (in order of usefulness):
  • Impact wrench
  • Impact wrench
  • Did I mention an impact wrench?
  • HVLP Paint Sprayer
  • Ratchet
  • Grinder

All were bought from Harbor Freight and have performed very well. While the impact wrench has been the most useful by far, I'm particularly impressed with how well the HVLP paint sprayer works. I got it on sale for $10 and it did a simply fantastic job on my brakes (to be fair, it helped that I used very good paint).

You didn't ask about non-air tools, but I thought I would share that the Harbor Freight snap ring pliers are pure and utter junk. DO NOT BUY. Northern Tool sells a pair of Channel Lock brand that are fabulous and VERY affordable (~$30 I think). I do regular tool reviews in my build thread if you care to check it out. Next one will be a texture sprayer (for thicker paints/coatings like Lizard Skin).

And again, welcome!