You can build up, own and buy prebans, except for those firearms which have been banned in CT by name.
You can't hunt with a silencer/suppressor. If you want to reduce noise, go with a bolt action 300 whisper or something.
Go see the guys at JoJos n Southington. Great guys and fully knowledgeable in class 3 and NFA stuff as well as AR's and firearms in general. I got my silencer through them and they explained everything and made it simple!