I've NEVER had an accident on my motorbike and I cover about 30,000 miles a year on it. My DP has never had an accident and many of our biking friends haven't either.
There is plenty of choice out there. You can choose something trendy such as a lambretta or aprilia custom habana (like Jamie Oliver). These don't have gears and are really easy to ride. You could have a cruiser (like a small harley davidson if this floats your boat).
Take your CBT and see what you think. My family were very against me doing it but once they realised that I was taking the proper courses and wearing all the protective gear they have accepted it and are now encouraging. In fact my Mum has offered to have DD for the weekend so DP and I can have our first bike weekend away in 18 months.
Yes, there are mad bikers out there, but it is like anything. There are good and bad, and you only hear about the bad ones.
Get yourself along to your local bike meet and have a chat with some people. Bikers are generally a very friendly bunch.
I only learnt to ride 6 years ago and I started with an Aprilia custom habana which doesn't have gears so I could gain road experience without having to worry about gears. Then I got a 125cc Yamaha Dragstar (harley davidson type bike) to get used to the gears. I passed my test and bought a BMW F650GS on which I learnt to ride offroad. Now I have a BMW R1150GS which is a great big bike which I ride confidently both on and offroad.
It's a great hobby. I would always recommend wearing protective trousers, jacket, gloves and boots as well as your helmet. If you go to somewhere like Infinity they do an own brand range which makes it cheaper. And, buy the most expensive helmet you can afford.
Don't know where in the country you are but if you let me know I may be able to put you in touch with someone you can chat to.