I think the 5500 is an excellent ski, so for you I would go in that direction. Based on your weight and height, I would lean towards the 181, although that would depend more on where you plan on skiing and what the conditions are. Take a series of lessons and you should see your skills improve at a rapid pace.
I prefer Marker or Salomon bindings, but I ski almost exclusively Atomic (because I pretty much have to). Something with a DIN of 10 and not a whole lot of bells and whistles should be fine for the Axis or 5500.
Boots are the single most important item. Spend your money there and get them fit properly. You don't need or want a race boot, but you shouldn't get a beginner boot either. Dalbello makes an excellent boot for the money, if you have a Dalbello foot. Footbeds are also an excellent investment, even if they are the pre-formed plastic variety.