You can use a ULA if you want to. That's essentially the IPv6 equivalent of a private IP.

Why though? Having the same IP for both internal and external solves a bunch of issues. For example, you don't need to use split horizon DNS any more (which is where a host name has a different IP on your internal network vs on the internet). You just need to ensure your firewalls are set up properly, which you should do anyways.