Really, deciding if you're kids can play this game all comes down to their personal tastes. I think it's a really interesting game but most early teens may find it boring or may not be able to deal with the darker themes. None of the previous games in the series have to have been played to understand the story, as the games are mostly unrelated. The game revolves around a serial murder case in a small Japanese town, and it's up to the player to find out who's doing it and stop them. This is really the largest source of violence in the game, as the actual combat isn't too gory. The player interacts with many students in their school and other people in the town (and a mysterious fox?!?), and gains social links to power up their "personas", the means of combat in the game. You can have romantic relationships with multiple girls, and there is little consequence to it. However, this is more of a gameplay contrivance than anything else, because to understand all the characters you must complete their social links, which with the girls is a relationship. There is a fair amount of innuendo and sex jokes, but no nudity and honestly nothing that wouldn't go on at a normal high school anyway. The same goes with the language, as it isn't as bad as most other M-rated games (i.e. no f-bombs). In one scene the characters(who are underage) do drink alcohol, and some items' names could be interpreted as drug-related. It should also be noted that most characters are flawed and through working together the player helps them become stronger, which is why it has good role models. Two characters both struggle with their sexuality, so younger players may be confused and not understand some of the discussions. All these are things mature teens should be able to handle.
Gameplay wise, Persona 4 is like a combination of Pokemon, a dungeon crawler, and traditional JRPGS. It is not easy to play for newcomers, but if you've played games such as Chrono Trigger or the Final Fantasy Series it shouldn't be too hard. What makes the combat unique is that players collect personas, each with their own unique stats, abilities, and weaknesses, and can use them to fight or fuse them to create more powerful ones. It can be overwhelming at first, but the game does a fairly good job of easing you into it and explaining what to do. If a player is struggling, they can always "grind" and go back to previous areas to fight enemies and become stronger. All in all, I don't think I could ever write everything there is to say about this game. The bottom line is that it has a great story, interesting characters, unique gameplay, and a long-lasting adventure that any mature gamer can enjoy. Now hurry up and announce Persona 5 Atlus!!!