If you visit the Immobiliers web sites or phone them directly (get the phone number from the resort web page or tourist office) you will find that they have plenty of apartments available for a seasons let. The rate for a season is significantly less than you will pay for each week individually, probably about half. If you have the time and could afford it I would also reccomend you visited the resort in the autumn to look at the accommodation yourself.
The next question is where.
If you want to sample the highlights of Apres Ski then clearly somewhere like Val d’Isere or St. Anton would be a suitable destination.
However, if you want to get the most skiing and the biggest possible choice for your money then in my humble opinion it has to be Bourg st Maurice. BsM is a real town (and because of this even its most ardent admirers would not call it pretty) with good supermarkets, lots of restaurants and bars, excellent rail links to the rest of Europe, even direct trains to London and of course a funicular upto Les Arcs and the whole Paradiski area at your immediate disposal. Within 30 minutes drive you also have the 3 valleys, Tignes, Val d’Isere, St. Foy, and the resorts straddling the Col de la madeleine and the Col du Petit st Bernard. For a day off you can even get the train to Chamberey or Lyon. Apartments here are also less expensive than the purpose built ski resorts.
One Christmas I met an old man in Les Arcs who even though he could barely walk always rented an apartment for the whole season. He skied a bit, relaxed a bit and enjoyed himself. Have a good time.
John