Just a little opinion I'd like to add to Bill's great post.
I believe that going with 15 breeding pairs would be preferable to four. The reason being that if there's any mortality, which invariably happens in fish transportation, you could end up with only one or two adults of a particular sex that provide all of the genetic information for your fish. If this is the case, any recessive genes which may inhibit growth or disease resistance will show up with greater frequency, which may lead to a condition known as "Inbreeding Depression". More genetic diversity is generally considered to be a necessity to a thriving population. It's been shown that even a few generations of fish isolated to a particular environment will begin to show preference to certain traits that give survival advantage. An example would be the McConaughy strain of rainbow trout, which occurred in just a few generations of reproduction within Lake McConaughy near Ogallala, Nebraska. The Feds actually have recognized, and attempted to preserve this strain because of it's uniqueness and the possibility that this strain would be ideal for other locations. If your pond begins with a diverse gene pool then there will be a maximum number of genetic characteristics available for generational selection. Your pond's "strain", if you will, may do particularly well in your pond's temperature range, pH, salinity, turbidity and foraging opportunities.
At this point you can assist the selection process by not harvesting your fast-growing, pellet-eating male bluegill. If you harvest your best fish then you run the risk of selecting for fish that reach reproductive age early before acheiving maximum growth.
You also may want to check the local regulations before transporting fish from your public waters. The C.O.'s aren't real fond of that around here
