12 years ago, I started with TWOK and I'm now married to her and she's a big fan (sees movies on opening night with me, goes to conventions, watched DS9 all the way through).
I'd say start there. For an intro, TMP is a little too slow (although we did go back and watch and she really enjoyed it). TVH is a little too atypical. TUC is a little too pretentious. Go with the "Khan Trilogy" then back to TMP. Then go forward with the others.
Worked for me.