Yes, the Alps are huge. But, as a start, I'd say that Switzerland or Austria is a good first choice.
There are a lot of ski regions linked on one pass, like the Arlberg, or the Zermatt / Cervinia area, Davos, Chamonix etc. they're all among some of the best skiing in the world.
Out of those, I highly recommend the Arlberg, it's easy access from Zurich Airport (2-2.5 hrs by train), and it's impressive terrain.
If you like Switzerland, the rail system has these "Ski and Rail" packages, or at least they did last time I visited, which is a combined ski pass for a couple of days + rail from various Swiss cities, so you can sample various resorts.
Also, with ski trips, the snow is no guarantee. I generally travel with the mindset of getting to know the culture better, trying out the food and the language, rather than going specifically for a 20+ inch dump. I've had trips that were icy / rainy the entire time, and I've had trips with insane amounts of snow.
