I need to buy a new toothbrush, and I wanted to know if any of those fancy designs make a difference? While we are at it, what about electric and battery toothbrushes? Are they worth the extra money?
IANAD but I think the best design is the one that you can clean your teeth with. 
I’m using a battery toothbrush right now and it works great. It was under $10 and the batteries are still going strong after 9 months.
To me, I feel my teeth are cleaner then using a regular toothbrush.
My wife (a dentist) says she likes Oral-B brushes better, but she used to receive a lot of graft from them. 
Really, she says the most important thing is how you brush, not the brush itself. She always chews me out for following Captain Kangaroo’s advice and going “round and round, three times a day” instead of up-and-down.
I’d like to know if the vibrations from the electric brushes can loosen fillings. I bought one and don’t use it much because I’m afraid of that. I have lots of fillings.
IANAD, either, but I asked my dentist about those fancy electric brushes and his advice was to keep on doing what I’ve been doing, which is using a regular toothbrush 3x a day. Years ago I did use an electric brush and I have a lot of fillings, and it didn’t bother them. If your fillings have been properly set, that little vibration is not going to upset them.
As previously posted, most important is how you brush your teeth and how thoroughly you brush them. Brush the bottom teeth up and down, but brush the top ones at a slight angle from the perpendicular. Be sure to brush the gumline. And brush them for at least two minutes, to ensure thoroughly brushing. Then use one of those metal hooks with a rubber tip at the end to massage the gums. (Those that are on some brushes are not as good.) Then use floss at least once a day. If you wish, you can finish it off with a swig of Listerine (which contains alcohol and kills germs).
More people lose their teeth due to gum disease than due to tooth decay. If you get a tooth cavity, it can be filled in. If you lose the gum support, you’ll need false teeth.