This is a two part question…
My UF installation would be accessed through mysite.com/public (which is the UF public folder)
Is this ok?
Technically, you just need to overwrite this constant :
It might produce unwanted behavior however, as this is not tested (at least I never have).
Another solution could be a symlink, either in your filesystem or Apache / Nginx config.
Is it best to use Nginx to solve this problem without modifying the UF source code to make it easier to update the UF version later?
Yes you are correct, using Nginx/apache would be the best practice and make sure it is easiest to update UF later on.