the data from CDC agrees with you, and agrees that a firearm is most common method.

but also indicates age correlate with freq of suicde by firearm.

guess who the least frequent group is, kids.

now that might fly in the face of stats, but suicide is an "intentional" thing. [that rides on the idea that you are competent to form intent when suicidal]

so yes if you keep your guns secure, and gun proof your kids to mitigate accidents that should improve things, for kids.

however take at least as much care for your grandparents, they are apparently at extreme risk, of forming intent and, acting especially grandpa.