That's a really tough question right now. The puzzle is that you're looking for a family console with longevity. Pretty much ALL consoles become more family oriented near the end of their life-cycle, as the price goes down and becomes more accessible to family budgets. But if, by "longevity" you want a console that will keep up with the latest releases and beyond, you won't want something at the end of its life cycle.
Normally, I'd point you to a Nintendo console. But the Wii isn't getting new games... and neither is the Wii U, really. (Nintendo makes games for the Wii U console, but almost no one else does.) This may be set to change entirely with Nintendo's new console, which they will be unveiling this coming summer. But it won't go on sale until probably next fall at the earliest, and there are still too many unknowns to recommend it. So that's no help if you want to upgrade this Christmas.
If by "longevity" you just mean a console that there will be plenty of games available to play on it for years and years to come, than the Wii, Xbox 360 or PS3 are each good choices. In which case I'd recommend googling "Best (insert your preferred game type here) video games" and following that rabbit how for a bit until you have an idea of where you will find the types of games you and your kids are likely to enjoy. There is a lot of crossover (I think Minecraft will even play on microwaves now) so it's hard to "lose" in this scenario. Unless you don't like the idea of waving your arms around while playing games. (Many Wii games are motion controlled.)
Feel free to give us more specifics on your preferences! I for one am happy to share my love of video games and help others discover their own!