There's a jillion posts out there on clipping in/out. What's most important is to focus and do it exactly the same every time. I unclip my left foot first as I am braking and put my foot down at the moment that I am at a full stop. Make sure you lean towards the planted foot -- either right or left. If you lean towards the foot that is still clipped you will probably fall. Keep a firm grip on the brake until you have full control of your stop or you will roll away with one foot clipped in and probably fall.
When you go to take off again, raise up the foot that is clipped in (for me it's the right) before you start. This give you a little step up to stand on while you lift yourself up to the saddle. You need to be able to pedal a stroke or two with your other foot just in case you don't get clipped in on the first try. Usually, you can rotate the crank a few times while you clip in the other foot. You may need to glance down at the pedal, but try to do it by feel. Glancing down could put you off balance.
If you have a nice grassy field you can practice in, try that. If you have the kind of cleats that work on a spinning bike (SPD), you could go to a spinning class and practice. Or put your bike on a trainer and practice.
Everyone falls. It is inevitable. I have had two falls in the past 1.5 years and both of them when I was just about stopped. I lost focus, leaned to the wrong side and down I went. Zero miles per hour fall, but still lots of road rash.
Good luck!
p.s. I am 58 and would hate to break a hip, too!!!
----------------------------------------------------
"I never made "Who's Who"- but sure as hell I made "What's That??..."