A lot of that will depend on the particular game. Like the number of people who can play at a time.
The one thing I would say, and it is fairly hard to find these days, but there are some places who seem to stumble across some units in storage somewhere and flog them at discounted prices. Make sure that you get one with the MotionPlus included. This is an optional add-on for the original Wii which adds a gyroscope to the Wiimote for the ability to sense whether the Wiimote is turned to the side, etc. If you have a cell phone or a tablet, and the screen rotates when you change the orientation of the device, that's because there's a gyroscope in the device.
Anyway, some newer games are requiring this in order to function, and it's not really much of a discount on an older Wii model if you just have to go out and spend whatever the difference was between the older model and newer one with it bundled. Plus, if it's a Christmas gift, you wouldn't want to spoil it by having the best of intentions in getting a game or two, and then one of them requires this add-on.
It's not common to find these older models in stores anymore, but just be sure to spend a couple minutes reading the box carefully for mention of MotionPlus or Motion+. If in doubt, go to a place like GameStop where the employees will likely be able to tell you which does and doesn't have it. Probably more so than your average big box retailer.
As for used games. It really depends on where you buy them from. If you go to a place like GameStop, then if the game disc happens to be bad, they'll swap it out for you, no fuss. I've also found GameFly to be a good place to buy used games, and have heard generally positive things about Hastings. Now, if you're buying on eBay or some such, all bets are off. GameFly might actually be a service you want to look into as a cost saving measure. It's basically like the Netflix of video games. Same basic model. You pay a flat fee per month, how much depends on which of the three service levels you want, and then you can have 1, 2, or 3 games out at a time. You can keep them as long as you want, as long as you keep paying your dues. When you're done, just pop them back in the mail, and they send the next one on your list out. You can also optionally choose to buy the game you have (with some restrictions on newer games) at a discount. Then you just keep the disc you have (which you know is good), and they mail you the case and manual for it. Also helps avoid getting burned on a game that seems really promising, only to be absolutely horrid in every way imaginable. If you get a stinker of a game, just send it back and move on.
That service might not make sense right away for you, but if the Wii becomes something of a staple in the house, might be worth considering.
An upcoming birthday present request is a Wii. Our family has never done any computer games before, so I'm starting from scratch here.
Let's just assume that we do want a Wii (and not other consoles like the PlayStation). What do you recommend? I've seen on amazon and ebay that used games aren't much cheaper than the new ones, but if I find a big gap, is it risky getting a used game?
We will want to use a lot of 2-player (or even 3 or 4, if that is possible) games.
I also see that they have an introductory bundle with the console itself for around $150, with most of the other games going for around $30.
Do they have deals where they sell you multiple games bundled with the console itself? Any other things a newbie should be on the lookout for? I do have a nice belkin wireless router; I've seen a wireless router mentioned as helpful.
Any suggestions would be appreciated.