You never try to put power into your punches. When you are hitting the mitts or the heavy bag, especially starting out, your focus should be on the technique, throwing each punch properly. That brings both speed and power. Personally, I'd be telling you to throw a punch slowly, in pieces, until the motion and the feel was comfortable to you (and I thought you were doind it right), and then to pick up the pace gradually. There's no point in doing it fast and wrong, no more than there is is doing it too slow.