Haha, I like that idea Nitrous. Just step out the back door and into the pool.
Finally got ahold of someone at DWR. For anyone trying backyard aquaponics, I'm going to keep updating all this permit info. Keep in mind that laws can vary quite a bit between states. The following only applies to UT, and only to my specific county.
Looks like I can get two of my top picks (channel cats and blue gill). Some of the other fish species are either completely banned (tilapia), or are not offered on the DWR's list of approved hatcheries, and therefore are not available to me. I can either apply for the private pond permit ($110, expires after five years), or the oficial I spoke with will extend an exemption certificate to us. The exemption cert itself is free, but the catch is that the fish would have to be delivered to my door by the hatchery, as I can not transport fish under it. So, now I will need to call around and see what the delivery prices are for the approved hatcheries, and see which one is more cost effective.