@houz’s advice is probably the best process. While you may not see a need for anything greater than 8-bit for final output, you’re right in thinking that intermediate operations done to the image will best be done with higher bit-depths.
This will give you the most leeway for pushing or pulling the tones around to suit your vision. Save any 8-bit result for a final export to, as you’ve already said, cover the widest devices for viewing it.
It’s no trouble, and is rather why we’re here in the first place! 
[edit] - in fact, @houz had previously produced a nice graphic to illustrate what’s going on:
