OP, while there are quite a lot good shows recommended here, I don't think all of them will be good for your father in order to make him like anime as a medium.

Recommendations below will be easily enjoyable by someone 30+.

First of all, make him watch:

• Death Billiards

If he enjoys this, you can continue with:

• Death Parade

If your father can excuse some (meaningful) nudity (not fanservice) and likes sci-fi, then give him:

• Cowboy Bebop

• Ghost in the shell

followed by either

• Ghost in the Shell: Stand Alone Complex

or

• Psycho-Pass

If he enjoys a bit of medieval / fantasy, make him watch:

• Sword of the stranger

• Berserk movies: 1, 2, 3 (warning: last one contains a very graphic rape scene, you better give your dad a heads-up)

Code Geass is out, it definitely is designed for a bit younger audience, plus has quite a lot of fanservice. Unfortunately Steins;Gate is also out, as it takes too much time to kick off. Baccano! is fun, but it might not be the best for a beginner adult. Death Note, while being very good overall, might not be attractive for older adults, because of the cast of characters.