Geez, you do have a bunch of questions...okeydoke.
1)When you purchase a Wii you receive, packaged inside, one Wiimote and one Nunchuk. You don't really need the Classic controller if you have gamecube one already though. Also, the Light Gun, aka Zapper, shell for the Wiimote was just used by Nintendo to show off how the Wiimote could be used in different ways and in different shells. It was, and hasn't been, announced for a release (yet). If you want another Wiimote I suggest buying Wii Play, it comes with a free one.
2)The straps that were released with launch Wiis were relatively thin, yes, but only idiots injured themselves with them. It doesn't matter now anyways since you can't get your hands on the thinner straps anymore. They were promptly replaced.
3)The best games are a matter of opinion, but I recommend Zelda, Warioware, and Trauma Center.
4)I'm not sure what you mean by "Box Set Thing." So I'll excuse myself from answering.
5)The Wii requires no physical add-ons, but if you want to use any of the nifty channels you'll have to do a system update via the internet. When you buy a Wii it prompts you to do so anyway.
6)The Wii is compatible with Gamecube games, but not the Game Boy Player attachment.
7)They cost as much as the Gamecube games did. About $50 American.
8)When you say all at once, do you mean simultaneously in the same room with other people? If so, yes. If you mean via the internet, not quite yet, but it is coming. The first game that will feature wifi play will be Pokemon Battle Revolution.
9)Here we go. The Wii has endless possibilities in this area. As of now you can look at the weather worldwide and get a 5-day forecast with the Weather Channel, check the latest headlines worldwide with the News Channel, vote in worldwide polls with the Everybody Votes Channel, go online with the Internet Channel, buy games from the previous gaming era with the Wii Shop Channel, and make little cartoon caricatures of yourself, your friends, and celebrities with the Mii Channel, edit photos and do puzzles in the Photo Channel, or send your friends a Wii E-Mail (or Wiimail) with the Wii Message Board. Anytime Nintendo comes up with another brilliant idea all they have to do is release a new system update, you download it, and bam. A new feature for the Wii.
10) Personally I give the Wii a solid 10. It is amazing in every aspect, and just keeps getting better with every update.
Hope I helped. :P Also, kudos if you actually read all that.