How do you plan on running the romex? Can you fish through the walls or will you have to surface mount?
Can you access the top of your panel without cutting drywall?
Also, is that a GE or Cutler-Hammer panel (they both have the same color breaker handles and I can't read the writing)? Also, what is the amperage rating of the main breaker (the big one in the middle.
As for the size of breaker you need, first find the HP of the motor on it, multiply the number of HP (true HP, not that peak HP **** they print on cartons) by 750, then divide that number by 220. Then add 20% to that number. This will be the size of breaker you will need (the next size up from that that is)
For 15 amps you need 14 gauge wire, for 20 you need 12, for 30 you need 10; and that should cover most home-garage sizede compressors just fine.
Code requires any motor over 1/4 HP to be on its own dedicated circuit, so this breaker will run go to one and only one outlet.