AI is short for "Ackley Improved." These days it's a general term for any standard case that's been blown out (fireformed) to minimal body taper and a steep, usually 40 degree, shoulder angle, whether or not P.O. Ackley ever actually improved that particular cartridge himself.
Left is a 243 Win Ackley Improved standing next to a standard 243 Winchester on the right:
Any non-wildcat cartridge is easy to handload for, you just need dies, brass and components. Wildcats are a bit harder because they need extra brass forming steps. AI's are easy if you shoot factory ammo to form the AI cases. After that, it's just like loading a standard case. Forming AI cases from raw brass is a little more involved, but not too hard.
What I think you might mean is "what cartridges are the least finicky to find a good load for?" This is not a real easy question to answer, but certain cases (or really case families) seem to have a reputation as being more forgiving than others (like the 308 Win family, for example). I've heard that some folks find that some of the really big magnum cases can be finicky, but others have no problems, so it's hardly conclusive. Basically, if the rifle is of good quality and there isn't anything wrong with it that precludes good accuracy (like a damaged muzzle crown), then you should be able to find a good load for it. Sometimes you luck out and nail one one the first try, and sometimes it can be a long and frustrating process. Just the way it is, but the results are usually worth the effort.
Mike