In reply to 1906johns:
Get something cheap.
Better still, for your first outings borrow kit from other people.
There is no "best" ice axe - what works for my body and my style might be brilliant for you, or it might be rubbish.
See how you get on.
For axes, weigh up the pros and cons of longer v shorter axes, straight v curved shafts, lighter v heavier. What sort of leash, or do you go leashless?
The Petzl website is very informative, even if you don't buy their kit
http://www.petzl.com/us/outdoor/ice-axes-0
As for crampons, the first thing is they must fit your boots.
I also set a lot of value to how easy they are to put on and take off - minimising faff is the way to go.
If there is no anti-balling plate and you are going out in wet snow, consider gaffer taping the bottom.