Safety stirrups vs normal stirrups?

what's your advice on stirrups? i'm buying a saddle etc. for my pony Fred for the first time (we used to borrow one but we have now moved yards so don't have that option anymore) so i am now deciding on which stirrups to buy. I was just wondering which stirrups i would be best to buy. My horse is a very nervous pony as he has been mistreated in the past by previous owners we think so he can be very jumpy and spooky hence me falling off quite a bit - it's a good job he's only 11hh bless him! I have had the experience of being dragged before when i was riding in small stirrups and it wasn't pleasant but from then on i changed them every time i rode from the child's stirrups into some adult stirrups and never had that problem really again. But my friend has those safety stirrups and i can remember once when we were riding when it all of a sudden pinged off (the elastic bit i mean) and it spooked all the horses. Apparently they are supposed to be good for if you fall off though so that you don't get dragged so i am really confused about which to get. Are the safety stirrups actually really reliable and did my friend just put the elastic bit on wrong? Or are they not really that reliable and would i be better just getting the correct sized normal stirrups?