Is the 16 go iPhone 6s enough if I don't download any music or movies at all?

More than enough

I still wouldn't recommend it either way.

Better to have too much space than too little

Just don't take any 4k videos, and ease up on the apps and pictures.

Yes and no. For music, it will be fine, but for movies, it depends on the quality of the video.

If you download 1080p movies, you'll run out of space fairly quickly. Personally, I'd try to get the 32Gb version.