Running the Freedombox in the DMZ is the easiest way to configure it. It is actually set up to automatically open firewall ports for the programs you install, so you don’t have to think about it too much.
As for your gateway, if you are feeling nervous about the security of your home network then log in to your router admin portal and close off any ports you aren’t going to be using for your stuff.
If you want a more secure way to proxy home, you can set up a SOCKS5 proxy over an SSH tunnel as described here, then the proxy would be relying on a tunnel established with password authentication or exchange of SSH keys that you have set up.
Anyway, I didn’t mean to scare you off of running your Freedombox in the DMZ. I hope I didn’t say something wrongly.