You really need a Wiimote for each boy, and I would honestly get a Nunchuck too. You might be able to get away with two Nunchucks at first and three later as many multiplayer games with Nunchuck control are two-player, but it really might be best to get them now when things will be on sale. Look at the back of each game you buy and there will be icons saying how many players, and if you need just Wiimotes or Wiimotes and Nunchucks for both. If your whole family wants to play at one (or rather, at least 4 of you), you'll need 4 Wiimotes.
The
Lego games are fantastic, even more so if you love the theme and Legos in general. My boyfriend and I (22 and 23) just picked up Lego Harry Potter and love it. The controls are simple enough and there aren't any real penalties for dying so your 10 year old can handle it, and the goofy in-jokes, smooth controls, and lots of stuff to unlock and collect will appeal to your older ones.
I have played the Star Wars ones, which you can get as one disk, Lego Star Wars: The Complete Saga or something. Early buyers like me bought each trilogy separately, so you're in luck! Lego Indiana Jones is also solid, and we're enjoying Harry Potter, though that one seems to have more "Learn the right spells to get through the level" as opposed to crazy brick-breaking in the older ones. I've never played the Batman one so I can't speak to it. They are two player so they'll have to rotate through, but that will happen with most games anyway.
Mario Kart is always fun. Super Mario Galaxy (and later 2 if they like it) is good as well. If you all want to play a good party game together, whatever the newest Mario Party incarnation is at this point is good. I think it's 8 or 9. They are big board games with lots of fun minigames you do to try and win the most stars.
Your older two will probably like The Legend of Zelda games, they are fantastic. Okami is also an odd Japanese inspired platformer/puzzle game, but it can be hard to find as the studio went out of business. Your younger one may also pick these up pretty easily, but I don't want to make any judgements. Some kids take to gaming like they were born with a controller in their hand, others may need to grow into it a bit.
My advice? Get
3/4 Wiimotes and 2 or more Nunchucks depending on the deals you find and the games you want, then do
1 Lego Game (2 players or 1 player, and hours of playability)
1 4 player game, either Mario Party or Mario Kart
1 Major one-player game Legend of Zelda or Super Mario Galaxy
Anything else at your discretion/budget
That, combined with Wii sports, should give you some easy casual games, stuff they can all play together (you and DH can even do Mario Party or Mario Kart with them), and a more challenging game for the 17 and 14-year old.
Other advice, be aware that if you get some gamecube controllers or the classic controllers, you can play Gamecube games on the Wii. So if you or they want to play something from Gamecube, you can. There are also lots of older games available to buy on the Wii Shop, but those tend to be from the old school Super Nintendo through Nintendo 64. It's a nostalgia thing for people like me who grew up with that, but some of the younger folks may just see bad graphics and not bother, without knowing what they're missing.
Also, since you seem to be new to video gaming, I will advise: if you're thinking about any kind of game that is a movie-tie-in, think before you buy! Most of these are crap which are made just to generate money off of a popular movie. Go online to websites like gamespot.com and read reviews of how good the games actually are. I would recommend getting reviews of any game before you buy it. Nintendo, while making the best games in the world, lets any idiot publish really crappy stuff for their systems hoping that unsuspecting buyers just take the bait.
If you want any more info, I'd be happy to provide it. If your sons have any particular interests maybe I can make additional game recommendations.