Well it sounds like you have a 60 amp subpanel then. Is this panel grounded, there needs to be 2 ground rods driven in the ground at the garage. Is it a 3 wire or 4 wire feed from your house panel? Is this feed cable from the house protected at the house by a breaker or is it a direct feed to the 60 amp disconnect.
If you decide to use any 14 gauge wires it needs to be connected to ONLY the 15 amp circuit. Use 12 gauge for the 20 amp circuit. The garaged door opener recpetacle doesn't need to be GFCI protected as long as its 7' above floor level.
You really need to buy a good book on electrical wiring. The Black and Decker home wiring book is a good start. You also need to check with your local codes as to what's allowed for a new breaker panel in this garage, alot of how a new sub panel should be wired will depend on the answer to the questions asked above.
Here's also an excellent link that'll give you tons of info of how this should be done depending on if the feed from your main panel is 3 wires or 4 wires.
http://www.selfhelpandmore.com/homew...rage/index.htm