I would definitely recommend Pokemon Diamond or Pearl. Great game(s). Phantom Hourglass and Metroid Prime Hunters are good. Animal Crossing is worth a pick-up, especially if you've never played the Gamecube version, you HAVE to pick this title up.
No, certainly not. I consider myself a mature 15 year old, and Animal Crossing from the Gamecube is still one of my favorites. When I'm done playing Halo 3, Oblivion, Call of Duty 4, or Super Smash Bros. Melee, I pop Animal Crossing in my Wii and it never gets old. It's such an addicting game, you have no idea until you play it. The DS version is basically the same thing but with an extension pack, which is why it's great for first-timers.
I have to make that my #1 recommendation if you've never played this franchise.
DEFINITELY a role-playing game. The time, holidays, and seasons that happen in real life...happen in the game. Basically you're a villager (male or female) where you get to choose the name of yourself and the name of your town, which you move into. This town consists of various animals who are your neighbors. They all have different moods and attitudes, which is awesome. Some of them leave and others fill their place. You can run errands for them and receive awards, buy stuff from the shop to you pimp out your house, etc.
The thing I love about it most is that you don't HAVE to do anything specifically. It has no "story plot". You basically have full control of the game and what you do. You can fish, catch bugs, sail, play soccer, decorate your house, get additions for your house if it gets too small, find fossils, as well as many other things (this is all MUCH more fun and less childish than it may sound). There are also special events for MANY things, but I'll keep that a secret.