I always do catered chalet hols as they're far more friendly than staying in a hotel, and you tend to get lots of very good food and reasonable plonk.
As for location it'll depend on skill levels. You can't go wrong in Courchevel 1850 especially for the range of skiing, but I prefer Argentiere in the Chamonix valley as it's a bit more nuts. Italy is better for beginners and those more interested in the food/fashion than the skiing with Cortina d'Ampezzo probably my fave. In Switzerland Verbier sounds like it's closest to your needs, but nights out can get very silly indeed....
You should be fine for booking for March. I rarely book before the week before, but I tend to only be looking for one room in a chalet. As far as companies go , I'd recommend Simply Ski for the mid-range budget and Collineige for the top end. There's quite a few very good small companies around so it's worth searching around.
Overall I'd say head for the Chamonix valley if you're not too fussed about having the skiing on your doorstep, Verbier if you want some serious apres-ski, and Courchevel 1850 if you want to spend every waking moment on the slopes.
Having said all that I haven't tried St Anton in Austria, but it always gets very good reports, and I've never been to the states as I don't like the idea of Ski police!!!
Have fun.
Ali