Actually I would hold off on upgrades at first.....just throw on the training gear and start sloooowly easing into basic hovering. That's what I did and I managed to progress from heli-noob to confident, steady tail-in hovers in my living room (still working on nose-in) with no more damage than a nicked up set of blades. Though I've had one serious crash since then........(pushing myself into fast forward flight too soon). One thing you might consider is upgrading the servos to Hitec HS-55's, supposedly that improves handling and precision a lot. I can't comment because when I bought my heli, it already had this upgrade, but it does sound like I'm avoiding some of the common control problems others here comment about with the Axe (jumping, mostly....I've started getting this a little, but never enough to be more than a minor nuisance).
The one upgrade I definitely want to get is a direct-drive tail rotor. Other than that, I'd suggest sticking with stock mechanicals. Put the $$$ into replacement parts as you need them (and you will...) and spare blades. Besides, plastic doesn't break as easily as those nice shiny CNC parts.

To be honest, I'm not sure I want to upgrade even the tail rotor, I may just put that money towards a better heli when I'm ready to move up. Something to think about when considering major upgrades to a somewhat basic heli.