So I've been looking through the forums on this topic and have one question on it;

If I breed 2 first generation, level 50 animals together (who have no GP and have had no children before level 50), then their offspring would then have 1GP...Is that correct?

Or does there have to be several generationsof good breeding (no inbreeding within 3 generations) to gain GP?

You are correct. ^^ The offspring will have GP1.

There are no secret hidden requirements to gain genetic power. Genetic power depends on the level of the parents and their GP and nothing else :D