In reply to WeeTJ:
It depends both on your height and intended activity. For more technical climbing shorter axes ( around 50cms ) are usually used whereas for walking / easier ground a longer axe may be preferred. Also, whilst you may be more of a walker now you might get an axe that is suitable for both walking and easy mountaineering that you may get into in the future. If that is a possibility it may be worth getting an axe that, at a later date, you could get a matching hammer for.
For walking one way to check the right length for you is to stand relaxed, with your hands by your sides. A walking ice axe in your hand would normally just touch or nearly touch the ground. My guess is that 50cms will be absolutely fine for you.