Exeter isn't a NATS airport, so you won't going there if you're applying through NATS. You can make a request for where you want to go, but the reality is that you'll be sent where the company needs you. If you end up as an Area controller, which is where most people go as there's more area controllers then you'll be in Swanwick or Prestwick. It could equally be Cardiff or Edinburgh though if you end up going down the Tower controller route
The initial training is supposed to be undertaken in Whiteley, Hampshire but they're now sending people to Spain for the initial training as well as there's not enough training capacity at Whiteley. Regarding commuting, it wouldn't be possible from Bristol, there's so much work in the first few months that you would really struggle.
I don't know what you do at the moment, but the starting salary isn't great and it can be three years or so before you start earning decent money which is something else to consider if you've got a family.