Is linked by USB or Thunderbolt best
I have a Buffalo 1TB external drive which is Thunderbolt/USB3 and I'm not convinced that the Thunderbolt connection is any faster than USB 3.0. However, if your iMac is only USB 2.0 then Thunderbolt will be faster.
The quieter the better! As it'll be beside us in our kitchen
External drives are not noisy, although a solid state drive will be silent compared to one with a spinning hard drive.
Can I save photos auto to a HD rather than on the internal HD?
I don't know the answer to that as I don't save photos to a Mac, mine are all in Dropbox. However, there shouldn't be any reason why you can't move them if you want to an external drive.