It has to be reliable. I will usuallly put a few hundred rounds through it before considering it for EDC and to insure that it has it's proper mechanical break-in period. Also, it gives me a chance to become more familiar with the weapon.
It has to be a proper weight size. Some people carry a full size steep pistol for EDC. I find them to be too heavy and will simply leave it home. I prefer a lightweight (somewhat compact) pistol for CCW. Through trial and error, one will determine a size and weight tolerance for their gun. (Personally, I find stuff over about 22oz too be annoying in anything other than a duty holster.)
It must be of a minimum/maximum caliber. The purpose of carrying a firearm is for self defense. It is important that it be chambered in a caliber to sufficiently stop an attack on your life. (My personal minimum is .380acp) Equally, it is important to have a caliber that you can shoot well and handle recoil based on the chosen platform. (I stay with .45acp or below for CCW.)
Sic Semper Tyrannis