Punch is based off of your unarmed combat skill and your Red bar.
You don't need any initiative points to use Jump or Punch.
Jump restores 12% of your Red bar. You'll need to jump about 8 times to have a full Red bar.
Throwing a bunch uses up your Red bar. The more Red bar you have, the more powerful your punch is.
For now, try to Punch and then fill up your red bar before you punch again.
If you miss, it means you did not break the enemies Blue bar entirely. That's okay! You want to whittle down their Blue bar over two or three attacks. After that you should land a hit.