You're restricted to cage traps only in this state. At the moment, you may use Conibears (body grippers) with a permit from the local board of health. This, however, may change if the so-called "puppy doe" law passes the legislature (I believe that it has already passed the house and is awaiting action in the senate).
As far as the trap registration number, you apply to the permit section of MF&W and pay a small fee for a number that is assigned to you forever. You must apply this number to your trap(s) permanently. In the case of cage traps, usually a tag of rustproof metal with your name, address and trap registration number is securely attached to the trap.
if you've never held a trapping license in any state previously you are required to attend a mandatory trapper education course before you may purchase a trapping license.
Not to take the wind out of your sails, but the wild fur market is at historic lows and probably will be for a few more years. If you're going to try your hand a nuisance animal removal, then good luck. The similarities end with the use of traps.