The original is a great place to start, especially if you don’t mind older media. The first 3 original movies are also exceptional. After that comes Star Trek:

The original is a great place to start, especially if you don’t mind older media. The first 3 original movies are also exceptional. After that comes Star Trek: The Next Generation, which is my personal favorite. If you’re still hooked, and don’t mind a change of pace and scenery (and in both cases, a slow start) Star Trek: Deep Space 9, and later Voyager would be the order for it.