Generally 2 good armor skills that will benefit you with switch axe is evasion + and evade distance. Evade distance is for mobility as your sword mode makes you as slow as a greatsword user and since you aren't going to be sheathing after every hit you will benefit from that. It also makes getting out of the way of attacks with the side-step much easier.
Evasion + is pretty obvious, you're a very offensive weapon so an evasion + skill will help you stick to a monster for longer.
Since I like to focus on getting the evasion skills before I work for offensive skills, my set progression is such: Lagombi for evade distance early, lobster for both evade distance and +1, some filler armor for initial high-rank, lagombi S with +1 gemed in, Stygian zinogre armor with distance gemed in and recover down gemed out. Stygian's armor can easily take you to G-rank from there as you get your evasion skills, a nice offense on the side and bonus dragon, and focus just doesn't hurt.
Probably not the most effective path, but it's worked for me.
As for advice:
I don't often recommend doing the idle X in axe mode. It's a powerful attack but it's also really slow if you just start with it. However if you use forward X, A, X+A, you will get quicker attacks which can help you get a combo going which then make that initial attack much faster making it wonderful if you can get into a good combo with this thing.
If you roll forward and hit X you will do an upward attack. It's a pretty nice attack and had massive upward reach. Don't be afraid to use it at all because it's a good way to get just jump in and start a combo on a monster since it also leads into the downward strike. An example of a monster this works well on are the raths. They go for in attack, you can roll up behind them and get a good attack or two off on their tails. They go in the air? Maybe if you give their feet a little tickle the might come down. In a recent azure Rath hunt I took that bastards put of the sky more reliably thay I've been able to do with flashbombs!