The server was setup as a service so we can only use btcpay on it. It seems though like it will be better to run our own server on a VPS maybe. This one is turning out quite limited.

Unless you mean the hosting on our server? That's a full control panel, you don't need terminal and there is softaculous installer for stuff like wordpress, forums etc. It's a standard web hosting account. We can do VPS as well but leaving that until we have this part up and running.