As much as I love striking, realistically in a fight if you connect with your fist, good chance it's going to break. Use of elbows or palm strikes/kicks are probably better options.
I wouldn't put too much weight in that thing about breaking your hand in a fight if you use your fist - especially if you actually know how and where to punch.
I'd personally say that a palm strike with a bent wrist (palm heel strike) is actually more risky in terms of damaging your wrist bones, which don't like being in that position. It also exposes the soft and vulnerable suicide spot - go upwards with a palm heel toward the chin, miss or slip and tear open your ulnar and radial arteries on their teeth...
Elbow? Sure, but it's a much closer range weapon.
Kicks? Fine, but you'd better be good, accurate and fast if you don't want to telegraph it to hell and back and get your leg caught (and this is coming from someone who considers themselves well on the way to being a 'kicker').