For the country:
Austria. Not only because that's where I come from, but because it's one of the main spots for skiing in europe, amongst Switzerland and parts of north eastern France.
Austria is cheaper than Switzerland, but I can't say anything about france, except that they have some very expensive famous spots.

If you plan to go to Austria, for skiing, then stay away from the very famous Kitzbühl. It's a posh place, were people show how much money they have (or don't have), but for skiing it's 2nd league.

I can personally recommend Leogang, which is close to Saalbach Hinterglemm (quite reknown spot), or Saalbach itself. My personal favourite is Obertauern (Salzburg Land). I go there myself every winter (only daily trips, as it's only 90mins drive from my home). The advantage is that they mainly have chairlifts or cable cars, which for beginners is much more convenient than t-bar tow lifts. In that area you'll find possibilities for beginners, as well as advanced skiers. Real Pros (and I'm talking about real pros from a skiing-country-inhabitant point of view) might feel themself a little unchallenged though.

The general areas for you will be Salzburg (Land) and Tyrol.