For what you describe (snow walking and general mountaineering)
you want a lightweight mountaineering boot.
Examples of such a boot are the Sportiva Trango S Evo Gtx, and the Scarpa Charmoz.
These boots are relatively lightweight, comfortable, and will accept crampons (although you will need to get crampons with strap fronts, as they don't have the front crampon lip.
With boots like these, you can do lots of classic mountaineering routes, and even take on the occasional steep front-pointing pitch.
There is a bit of information on mountain boots on my blog, here:
http://www.larsonweb.com/boots/
The Sportiva Makalu or Manta are other decent options.
It may be difficult for you to get a proper fit via mail order from the US. I would highly recommend buying local. If you truly can't find what you need locally, I would suggest buying 4 pair of boots, (2 different models, in 2 sizes each) and planning on sending 3 of them back.
Here are some New Zealand options:
http://www.gearshop.co.nz/index.php?main_page=product_info&cPath=2_118_121&products_id=537
The New Zealand distributor for Scarpa: http://www.allsports.co.nz/
The New Zealand distributor for La Sportiva: http://www.marvelox.com/
http://www.livingsimplynz.com/footwear/women_s/alpine_boots_womens
(the Makalu, and the Berghaus options on this page would serve, although the Makalu is significantly heavier.)
http://www.outsidesports.co.nz/Product/AL71002/Scarpa-Manta-GSB
Here are some USA options:
http://www.sierratradingpost.com/scarpa-manta-mountaineering-boots-for-men~p~2015n/?filterString=search~scarpa%2F&colorFamily=01&merch=-2015N
(Decent all around non-technical boot.)
http://www.sierratradingpost.com/scarpa-summit-gore-tex-mountaineering-boots-waterproof-for-women~p~2015p/?filterString=search~scarpa%2F&colorFamily=01&merch=-2015P
(This boot is a little heavy duty for what you want to do, but it is a terrific mountain boot and will be great for more technical climbing if you go that route. Also reasonably warm. Price is amazing on these.)
http://www.sierratradingpost.com/scarpa-triolet-gore-tex-mountaineering-boots-waterproof-for-men~p~2015k/?filterString=search~scarpa%2F&colorFamily=01&merch=-2015K
(a good choice if it fits)
http://www.sierratradingpost.com/scarpa-charmoz-gore-tex-mountaineering-boots-waterproof-for-women~p~3408y/?filterString=search~scarpa%2F&colorFamily=01&merch=-3408Y
(Probably the ideal boot if it fits.)
http://www.sierratradingpost.com/scarpa-freney-xt-hiking-boots-for-men~p~74683/?filterString=search~scarpa%2F&colorFamily=70&merch=-74683
(Again, probably the ideal boot if it fits.)
http://www.sierratradingpost.com/mammut-monolith-gore-tex-mountaineering-boots-waterproof-for-women~p~3933w/?filterString=climbing~d~9%2F&colorFamily=01&merch=-3933W
(Another great option, with a large range of smaller sizes available at a good price.)
http://www.sierratradingpost.com/asolo-broad-peak-climbing-gore-tex-boots-waterproof-for-women~p~1806c/?filterString=climbing~d~9%2F&colorFamily=01&merch=-1806C
(Good, relatively light weight technical boot.)
On the question of ice axe length, I'd say that a 50 cm tool is probably the right length for you.
A tool like the Black Diamond Venom is a nice all-around tool that is good for both general mountaineering and classic steeper routes. The replaceable pick means that you can just change out picks if you snap a pick, rather than having to replace the whole tool.
http://www.blackdiamondequipment.com/en-us/shop/climb/ice-axes-piolets/venom-ice-axe