I am going to assume you googled safety issues with trampolines and have read the story of the mom who was standing by the trampoline and heard her son's neck break as he died. I am going to assume you have read the American Pediatrics Association reports that say home trampolines are the cause of over 100,000 injuries to kids and teens each year and they would like to ban selling them to individuals. I am also going to assume you have called your home insurance to find out how much your insurance will go up with a trampoline on the property, or if they even allow one at all.
The nets can cause teeth to be yanked out, fingers to be broken, all kinds of pull injuries to appendages that get caught, the nets are not safe, they are more dangerous than not having a surround at all.
If you do decide to have one then always make sure the kids only jump up and down, no tricks whatsoever. it only takes them turning their head one way or another. It only takes 1 fall to break a leg, or the trampoline cover to bounce against the bottom of their foot wrong to break the growth plate into pieces.
Just keep googling trampolines and trust your heart.