A minimum maneuvering speed is just that. It is the slowest speed at which you can maneuver, which means you can exceed 15 degrees and go (usually) to 30 degrees. Slower than that speed, you must restrict your bank.
As far as the safe altitude to initiate a turn, that's a little subjective. If you are nevernever going to experience any engine problems, control problems or obstacles, then I suppose a case could be made that you can turn as soon as you're safely airborne. On the other hand, ...............