In what order should I watch the Ghost in the Shell series? The Ghost in the Shell series is comprised of several movies and animated TV series.

TV series:


Ghost in the Shell: Stand Alone Complex
Ghost in the Shell: S.A.C. 2nd GIG
Ghost in the Shell: Arise


Movies:


Ghost in the Shell
Ghost in the Shell 2: Innocence
Ghost in the Shell: S.A.C. 2nd GIG – The Laughing Man
Ghost in the Shell: S.A.C. 2nd GIG – Individual Eleven
Ghost in the Shell: Stand Alone Complex − Solid State Society
Ghost in the Shell: The New Movie  


For someone completely new to the series, what order should these be watched in? (Are the movies even important to the animated series?)
Here's the order:

Ghost in the Shell (set in 2029) from 1995 or its 2008 remake Ghost in the Shell 2.0
Ghost in the Shell: Stand Alone Complex (set in 2030)
- The Laughing Man, a feature-length OVA summary of S.A.C.
Ghost in the Shell: S.A.C. 2nd GIG (set in 2032)
- Individual Eleven, a feature-length OVA which retells the events of S.A.C. 2nd GIG, altered to focus on both the Individual Eleven investigation and the relationship between Hideo Kuze and Motoko Kusanagi
Ghost in the Shell 2: Innocence (set in 2032)
Ghost in the Shell: Stand Alone Complex − Solid State Society (set in 2034) from 2006 or 2011 in 3D
Ghost in the Shell: Arise OVA series (set in 2027). It's a prequel telling the origin story of Section 9
- Ghost in the Shell: Arise - Alternative Architecture is a recompilation for television of Ghost in the Shell: Arise.
Ghost in the Shell: The New Movie is a movie set after Ghost in the Shell: Arise that is a continuation of the plot of the Pyrophoric Cult episode. The original movie's plot follows directly after this movie.
Ghost in the Shell: SAC_2045 is the next and latest anime and follows all the other seirse for this anime series

The only unclear part is about where S.A.C. 2nd GIG and Innocence go in relation to each other, because they are both set in 2032. 2nd GIG is the second season of S.A.C. and should probably be watched directly after it.

The GitS movies, SAC-series and Arise OVA are all different interpretations of the source material/manga.
Ghost in the Shell/2.0 and Innocence are set in the same universe, and I would recommend to watch them first as they have the strongest story and production values.
The SAC-series has it's own separate universe and is more of a crime series where the movies are more philosophical.
The Arise OVA-series is also completely separate from both the movies and series, but somewhat serve as a spiritual prequel to both.