Hi, I'm new to the forum but certainly not to horses. The Tom Thumb is pretty much the standard western trail bit - but then most western horses neck rein. The TT, to answer another's question, is a snaffle with shanks that allow for the use of curb strap.
If you want the extra control the shanks offer then try one with a Billy Allen mouth piece. It is similar to the TT except that the two halves of the mouth piece are joined by a "barrel" so that they move independently and one side does not effect the other.