One with a lid with locks or clamps. And I'd recommend a room with a door where kitty can be locked out so they aren't freaking your tort out by hopping on the cage.
My tort was previously malnourished and her beak is forever damaged from this - I have to take her to the vet and have them shave it down
Your torts will continue fighting - I totally understand where you're coming from, I too am under 18 and live at home, I'm planning on building a double enclosure soon, stick to your guns make sure they know that you know what you're talking about and your torts are in danger