Just realize that all the 24th century spin offs are DRASTICALLY different than TOS. In look, in feel, in story telling, in every way possible they are apples and oranges. TOS is much more action/ sci-fi adventure oriented...rent the remastered version if at all possible. Gorgeous new FX have been added and the episodes have been digitally restored. The others are more modern and have better construction of sets but tend to be a bit talky with less emphasis on the adventure/fun side and a heavy reliance on technobabble (made up technical terminology that doesn't really mean squat!)
My advice is to sample both, but be prepared, the original Star Trek and multitude of spin-offs have as much in common as Happy Days and Mork and Mindy.