I want to re-answer in a less traditional way (it wasn't really one person, and definitely not family as I said earlier).
In addition to always eyeing my grandfather's guns when we'd visit as a kid, the biggest influence on me getting into guns (as opposed to how I collect, train and practice as a gun owner) is the US soldier and my love of history. I read my first book on WWII when I was 8 (I remember my parents being upset at the school library for letting me take it out as they thought I was far too young). When I was 8-12 I would read about the Revolution and daydream about being one of the Minutemen. I especially loved reading about the Civil War, WWI and WWII (Korea was "The Forgotten War," I read about it, but there simply weren't as many books about it for me to read, and Vietnam was still fairly recent history when I was a kid and didn't have many books about it yet... I did read what there was though). As I got older, I continued to read as much about military history (not just our wars) as well as all our major wars as I could (I still do, though I simply don't have the time to read that I used to have). I know my love of military history had a huge influence on my joining the Army after high school instead of going straight to college, and it also had a big influence on my developing an interest in guns even though I didn't start buying them until some time later.