Axe combo's are kinda annoying, but then again half the reason is because i'm trying to find new ones. His current stuff is mostly easy to do, the only real exectuion barriers i've seen outside the norm are-
1. Teleport combos. There's really only one that i know of and it's not required, so i wouldn't even worry about it until you're more comfortable with him.
2. Comobing while invis. You HAVE to look at your opponent for visual cue's on links, because i honestly think that one of ares biggest advantages is eventually going to be invisible mixups. If you really want to get good with him, don't look at him for visual cues on the tougher combos, and instead watch where the opponent is.
3. Meter management. I personally have a hard time getting certain sword/axe moves to come out, and it doesn't help that you really need to know when you can and can't use them since it's a huge part of his game(can't really threaten off a low otherwise). Further he really doesn't use meter in combo's like most(he's using down sword instead) so intelligently using the meter he has is important and probably required. Armoring b3/f3, push block, and the occasional EX pound/fireball/invis are all required. There may eventually be stuff that wants the bounce cancels as well.
Still all of that is top of the curve stuff. As a pick up and go character he should take about a week of casual play tops to get down for friends.