Welcome, GamerDad! My son and daughter have both been playing some form of RPG for years, from the natural beginnings of the kid-centric D&D4-based "Heroes of Hesiod" adventure (which I then expanded into a game system I called "Monster Battlers") through diceless RPGs to D&D5 this past year. My son, who is now 12, is running his first game as DM now; his sister and I are playing in his custom dungeon adventure. I can say with absolute certainty that his skills at role-play are WAY more sophisticated than mine were at the same age.
As Jabes.plays.RPGs and others suggested, the Games Tavern thread is a good place to check for games with openings. I may post another game there myself, soon.
With regards to type of fantasy RPG you enjoy, are you more interested in character-driven stories/role-playing, more interested in the tactical elements of combat/solving puzzles, more interested in blowing off steam with humor, or more interested in exploring a game world and the plot of a campaign?