You've got basicaly 3 options for lodging. Hotel, appartment and residence (like an appartment but with some extra services like a bar or a lounge, laundry, sometimes a restaurant... in-between and hotel and a flat). The best value is the appartment, then the residence then the hotel : more services = more Euros... A 2 stars hotel should go for something like 100 to 120 Euros a night, HB, (but you should get a rebate a long stay), when you can rent a studio in a good and well situated residence for probably 500 to 600 Euros a week (in january) and have a flat for less than that.
Problem is most (if not all ) residence or flats are rented only on a weekly basis. If you intend to stay 1,5 week this could be a problem. Maybe is it negociable in mid-january (a low season).
About the ratings : a 2 stars hotel offers really good comfort (bath room, breakfast, TV...). You'll find the room smaller than in your average US holiday Inn, but some 2* Val hotel are charming and well situated, like this one http://www.hotel-lauzes.com/welcome.htm
. To upgrade to a 3 or 4* stars will bring you a larger room and extra services (like a pool, a sauna,a jacuzzi...).
I've actualy never stayed in a hotel in Val, but I know where they are and I can get infos on most of them, so feel free to ask if you have one in mind. I'll check it out to give you suggestions and will update.
Anyway, you most certainly should look for tour operators packages. You'll find a long list of US operators on Val d'isère's site. For what I know it's a widely popular option among UK visitors because of the bargain prices they offer. To book things on your own will surely be more expensive.
Anyway, make sure to stay in the 'village' and avoid 'la daille' (a concrete condos ensemble down the road). 'Le fornet' is also OK, a small and quite nice hamlet up the road. Not very lively, but pretty.
How to get there : 3 options:
You may fly to geneva and transfer by taxi or bus. A 4 hours drive. or by helicopter (don't know the price though...)
You may fly to Lyon, 3 hours transfer by taxi or bus (longer distance, but better road in winter).
You may fly to paris and take a train to Bourg saint-maurice (5 hours during the day or an 9 hours over-night trip in a sleeping car, plus 1 hour to transfert from airport to the train station). The transfert from Bourg takes less than 1 hour, by bus or taxi.
It all depends on the prices you'll find and wether or not you can find direct flights to Lyon or Geneva. (or if you intend to visit paris or Geneva...). I guess Geneva is your best bet coming from the US. But I know they're direct flghts lo Lyon from the UK, so ..? And don't rent a car, it would be useless once in Val, and parking is expensive.