I've used SPD's for years. My mate describes the extra power you can utilise going up hills as "having an extra pair of legs" and I'm inclined to agree. It really does make a BIG difference and pedaling in circles is far more efficient when on the flat.
As mentioned in the post above, a good way to start is by riding around on the grass on the flat where you can practice starting and stopping. I didn't fall off much when I first started out and it really does become second nature. I would go for the multi release cleats though and set the pedals up with low tension when you start out, then gradually tighten them up as you grow in confidence.
I actually feel much more secure riding clipped in down hill or up. Bear traps or flats with pins make a horrible mess of your shins when you slip off and in my experience the injuries tend to be far worse than the injured pride you might get if you fall off the first few times you ride SPD's. Bear in mind unlike slipping off a flat when travelling at speed, if you do fall over because you have forgotten to clip out, you will be virtually stationary and it doesn't really hurt.
Stick with it and you will reap huge benefits.
94 GT RTS 3 (in build)
05 Cinelli estrada
93 Saracen Ltd Edition - In need of love
93 Ozone O2 E-stay (the wife's)
2013 Whyte 129-S
2016 GT Grade