.380 acp is the minimum I would carry...9mm preferably. Size of the pistol really depends on you...your size and how comfortable you are to recoil. Also, depends on how you're going to carry...concealed or open. Pick the pistol that fits & shoots the best for you.
The reason why even Veterans have to go thru a CC License to skip background checks is because even Veterans have Criminal Records that deny them from owning a firearm. One my best friends from the Military had a retraining order put on him by his pos ex wife...can't own a firearm.