People are now saying how dangerous trampolines are, yada yada. If you look hard enough you can find something dangerous about almost everything kids do. Maybe you can keep you and your family safe if you just live under a rock or something.
That said, I grew up on a trampoline with no special netting and no pads around the springs. We never had any injuries. WE WERE TAUGHT SAFETY PROCEDURES....imagine that.
We've had a trampoline at our house for our daughter, now 13, and it has been well used, no injuries. Kids FOLLOW MY SAFETY RULES or they DO NOT JUMP. Our trampoline does have the special netting and padding.
We have neighbors with both a trampoline and bounce house. The children love them. Just supervise and teach the children the right way. Accidents are going to happen with many activities. What are you going to do, have no pool, no bike, no scooter, no swingset, no roller blades, etc etc