What's the best style of wine to bring to a holiday gathering?
The safest bet is Champagne or another good sparkling wine (especially if you're coming to my holiday gathering).
A wine gift should flatter the host, and bubbly is always welcome, especially with New Year's Eve approaching.
If it's a dinner and you expect the wine will be served with the meal, ask if you can bring something to match the food. If, on the other hand, it's more of a cocktail gathering and you are talking specifically about a gift to be consumed later, in addition to Champagne I'd suggest a European red, such as good Côtes du Rhône or Chianti. These tend to be affordable (mainly in the $15 to $30 zone, though some are more expensive) and would please most people.