You might want more advise then just my own as I have yet to hunt deer with my own 300 Whisper. Just the same, I think that you would be very wise to consider the Single Shot Pistol bullets in the 125-gr range as being very good big game bullets.
As for the barrel length, with the 300 Whisper there is so little powder being burned this really is a non-issue for a rifle. A 16-inch barrel is the shortest you can have unless you wish to register it as a
Short Barreled Rifle
As for the twist rate, if you will never shoot subsonic loads then the standard 1:10 twist barrel is fine. If you are getting a barrel from T/C it will be 1:10 (or is it 1:12?) as that is the only twist they make. If you want to shoot subsonic loads then you really need a 1:8 twist barrel!
The 1:8 Twist barrel will work with all bullet weights while doing better with the heavy bullets while the 1:10 twist will only work with bullets upto about the 180-200-gr weight but it will give better performance with the 125-150gr bullets you will be hunting with...
Hopefully you will get other oppinions as well!