The only things the first two movies and the anime have in common are the characters. You really won't miss anything if you watch the series first then the movies or vice versa.
The series is kind of important to watch in order, since they do mention stuff that happened in the first season a bit in the second season. The second season also has a lot of back story that really made watching the whole series worth while. Definitely watch the whole series before you watch the third movie or else you will be completely lost. The third movie is actually the first and probably last movie of the anime and has absolutely nothing to do with the first two movies.
As for the movies, definitely watch the first then the second, or you might be wondering why certain characters are absent and why.
Ghost in the shell as a whole is amazing, and I'd recommend it to anyone. I just wish there was more ....