I wore NATO in the early days of my military service. I learned quickly that in highly active environments, NATO straps stain from sweat and collect dead skin that you have to clean regularly or it starts itch and smell. I'm sure for casual wear, it's not much of a problem, but my experience left me a bit tainted.
That said, a soft rubber strap warms up to the skin and secures the watch nicely in place. Original Seiko straps used a rubber that was quite hard and not so comfortable. I don't know about modern Seiko rubber, but hopefully they use better compounds today.
My recommendation would be to find a quality rubber strap, especially if you're very active or expose it to water. If not, even a nice leather strap would work.
So that's my two cents worth. Good luck with your decisions and be sure to share photos!