Clipless will definitely help your climbing. Here are a few suggestions for a clipless beginner.

1. Set your clips really loose.
2. Practice with your bike on a bike stand.
3. They make some pedals that are big platform pedals that have a clip. The platform is big enough to stand on unclipped. This is good for a beginner. You can upclip on technical down-hill sections until your confidence grows. I think there are also some that have a clip on one side and not the other. The problem with these is that you can't just clip in instantly, you have to look to see which side has the clip.
4. Keep your pedals clean and lubed. If you don't lube them, they get harder to "clip out"
5. You WILL fall. Be prepared. As you start to do the "timber" thing, try try try not to put your arm out to break your fall (broken wrist or worse yet, collar bone). Try to tuck your arms in and roll onto your shoulder. I know it goes against your natural instincts, but you will probably be better off.
6. To see how much the clips will help, try taking a spin class with and without clips. You can tell how much more efficient your stroke is if you make "circles" with your feet instead of just mashing down on the pedals.

Good luck and go have fun!