Your local server is probably running Apache (or some other lesser-WordPress-friendly web server software), so the Apache you’re moving to shouldn’t be part of your “concerns”.
That said, I personally prefer to work with my actual domain on the local machine (rather than using localhost). This way, I don’t have to bother with changing URLs when I move the site to the Internet. You do this by configuring your computer’s “hosts” file to resolve the domain to your machine’s private/localhost IP address.
As you already have the localhost address in your URLs, one option would be to use a migration plugin that allows you to change the site address during the migration. I believe “All in One Migration” does this.
Finally, if the migration tool you use doesn’t allow you to change the domain during the migration (eg say you dump and import the SQL directly), you can easily change the “site address” of your WordPress site after the migration by following this guide:
Changing The Site URL
It’s this possible without braking the perm links structure?
You can easily set/change your permalink structure with just a single click from the dashboard, so I wouldn’t worry about this even if the migration doesn’t retain the local site’s permalink structure. As long as the before and after permalink setting is the same, the URLs should be consistent (after changing the “site address” part, as described above.)
I hope that helps!