If you learn from a Karate guy, make sure he has put in his time doing full contact fighting. Most Karate guys can't punch through a wet grocery bag. I know this cause I fought full contact for 5 years.
In general, you need to land the punch with the knuckles from the index and middle fingers. This is the migari punch. Much harder part of your hand. Also, keep the wrist very stiff, and keep the elbows in (when throwing a jab or straight line reverse punch). You should punch from wherever your hand happens to be, do not rear back. If you try that shit against me, I will have you tied up and your arm broke before you have time to even deliver the punch. Do that against a wrestler, and you will be double legged and dropped on your head.
Besides, you don't hit any harder when you rear back and it is horribly slow, so don't do it. Elbows in, throw the punch as straight as possible, and don't hit at the nose. Try and hit the back of his head, but go through the face to get there. When hitting to the body, try and hit his spine by way of his belly, get the picture?
I would recommend finding a gym that teaches boxing. Boxers are the best punchers out there anyway. And boxing, along with grappling are much more useful in life than a traditional Karate school education. I am very thankful that I had a teacher who knew how to fight and was only interested in training fighters, but it seems like guys like that are very hard to find. Most are only interested in selling you overpriced gear, and charging you hundreds of dollars every few months to take your next belt test.
My 2 cents, hope it helps.
B.