The Watch subseries mentions vampires quite a lot, and is a really good read. IIRC, the fifth elephant and thud! Have them as more than just ‘extras’ and names mentioned.

While you can pick up most any discworld book as a first one, and have a good time, a lot of people recommend reading at least the sub series in order, the watch series starts with Guards! Guards! And is really enjoyable all the way through, and a great place to start your discworld journey.