A cage would be much much cheaper then completely chin proofing a room in a house. If the chins are living in a room you want to make sure there are no outlets in the room, the walls need to be something chew proof, they will eat drywall, your best bet would be cement or brick, or tile the walls. You would also need the floor to be something chew proof and water proof.
A baby gate will not contain a chin, unless you find one that is 6 feet high, they can easily jump 5 feet. A door would be best, but since you can't see through a solid door you'd need a metal wire door or something, so you can see through it. It has happened where someone had a chin out and someone else came in the room hurting or killing the chin with the door, not knowing the chin was by the door.
Another thing you didn't mention is the air conditioner. Unless you live in a place that never gets above 70F and never humid, year round, then you will need an AC. The AC would have to be high up on the wall with no shelves near it, and with the cord probably inside the wall, not accessible. Unless you have central air with vents in the ceiling, then just no shelves near the vent.
However, you can pretty easily "chin proof" a room enough for supervised use. Have them live in a cage, but let them out to play in a room when you are there to watch them and prevent them from chewing on things they shouldn't. You don't need to worry about them chewing the walls or floor as much if you are there to stop them.
Another option I've seen is basically making or buying a walk in style cage, so not a whole room but most of it. Something like
this, but set up for chinchillas. You could have it away from the wall so they can't chew it or access any outlets. Or if you are handy you can make something like
this, and you and make it as big as you want. It's still a cage, but a very big one.