Don't have my books on me so I'll double check this when I get home tonight, but...

Having Strength 20 and Fighting 0 means you can't punch anything but can left pretty much anything of course anything you throw is going to do at least your strength in damage!

Ideally you might want to think about Strength based Damage which is 1pt per rank and adds to your Strength score for damage purposes so say Strength and Fighting at both 5 with Strength based Damage at 5 to do 10 close damage for 5 power points instead of 10 to have your character strength at 10 for the same effect.

Check out the Accurate modifier which gives you +2 to hit with your Strength based Damage per Accurate you go for as its most often used to counter the penalties for multi-attack.

Be back later.