Are you currently with Virgin Media or something? You aren't obliged to leave your existing Openreach modem in the property when you move out.
As a modem or as a router?
It's quite possible it can be bridged to act as a modem but that would make it expensive for that usage.
You’re talking about marginal differences. You aren’t going to have a situation where a HG612 isn’t going to work.You can't just blanket say HG612, it's dependant on what chipset is in the cabinet.