The best way to tell which types of vermouth you like and how you want to use them is to taste a few and see which ones speak to you most. Aside from the differentiation between dry and sweet vermouth, there are also a ton of different substyles, flavors, and brands. Having a basis of what to expect and what it is you’re looking for can help you figure out which ones to try first.
But before you start opening up a bunch of vermouth bottles, know that it is used much more commonly as an additive in cocktails and sometimes food recipes than it is as its own sipper. Sometimes, however, you can enjoy a bit of vermouth in a glass over ice, which is an easy way to really get to know its taste.
Bon Appétit mentions a few of the herbs you might taste when sipping vermouth, like saffron and juniper, as well as a few key differences among dry white, sweet red, and sweet white vermouth. And, since everyone’s tastes are different, you might enjoy vermouth much more than someone else; this article by Bon Appétit also includes a fun diagram of celebrity vermouth-to-martini ratios, to give you an idea.