If you're looking for an explanation as to why max excess thrust will give max angle of climb and max excess power will give max rate of climb, you need to go over a TON of basics. Thrust and power are connected somewhat like torque and power. I wrote an article on torque and power that you can check out here:
http://www.box.net/shared/tpby1m893e6mipiv6sjp
When you talk about climbs you have to discuss power required and power available and thrust required and thrust available. I find it's best to start with power when discussing reciprocating engines and start with thrust when talking about jet engines. It can get incredibly confusing so take it one step at a time. The Advanced Pilot's Flight Manual has some good stuff on climbs that I suggest you read. You've asked such a broad question it's impossible to answer on here. I could write a book on it. Once you've read that and understand it a bit, I can help you with specific questions.