The Haute Route is a classic route from Chamonix in France to Zermatt in Switzerland. The cost will depend on what time of year you go and if you organise your own trip or take a guided tour. A guided tour is by no means essential for experienced off piste skiers, though having a guide will be able to tell you what mountains you are either climbing, skiing down or looking at. Huts can fill quickly in peak season.
You must be a strong skier. Inexperienced off piste skiers should not take this trip. Even experienced piste only skiers should definitely take a guide to make sure they are safe while skiing the route. Although its hard to get lost , the avalanche risk can be extremely high and the terrain in Europe is much more extreme than anything you are likey to have skied in North America. A guide will get you through safely and choose a route reflective of your ability.
So much depends on the weather. If the weather forecast for when you are planning to take this tour is anything other than perfect you should seriously consider scrapping any plans you have made.