The first thing you have to consider is whether you like your bubbly sweet or dry. The two main classifications are Extra Dry, which is sweet, and Brut, which is dry. I know, it's funny.
I like my champers dry. My favorite mainstream brand is Taittinger. I think Dom Perignon is overpriced. Cristal is too floral for my taste; I prefer the nuttiness of Taittinger. Veuve Cliquot is also yummy.
Rose Champagnes are considered by some the finest. Cristal Rose is absolutely wonderful and one of the most expensive.
There are dozens of lesser-known labels that are good. Happy New Year!
QL