A 410 is pretty small for any type of self defense. What I recommend is a Remington 870 lightweight Pump 20 gauge (shorter stock etc). My daughters each have one and can handle it fine. With #6 shot at close range it is devastating. A low shot at someone in the house would certainly take there legs out. Center of mass hit would be hamburger.
It can also be used with slugs for a longer range weapon. I have killed deer at 100 yds with my daughters guns. This is with a smooth bore barrel and I practice at that range.
with a 410 I would recommend to start a youngster out with 8-12 yrs old.

Huck