My turn!
1) all the same reciever regardless of model. The "K" models usually thought of as stainless, still have the aluminum reciever.
2) Some "T" models have been a bit better supposedly. I've found that for the money the nest deal is to simply send your entire trigger assembly to TT Shooter and for $80 you get one of the best feeling trigger's out there. HIGHLY regarded over at Rimfire central -
THE 10/22 site.
3) It's worth what someone is willing to pay for it. The older Walmart models will get a bit more now but not so much as to make them a good investment, especially if you're gonna use it.
4) The "carbine" model is simply the standrd length models. The 20" and longer models are "rifles" and the new 16" model is the "compact". other than the bbl length and the reciever markng, only the barrel band differes on the models. The compact of course also has a shorter length of pull stock design.
5) For the price, might as well buy a new one. Used ones won't save you very much anyways. Even used they get close to new prices just becasue so many people buy them just for the recievers to build up.
Now, after all that...I'd think maybe starting with a standard carbine model of maybe the rifle. It'll come with a scope mount and sights. As interst rows you can add a scope (Simmons .22 mag series is good and inexpensive). If there continues to be interest. You can add another and your wife or son or both as well s you can customize and build them up as you choose. There's a nearly endless amount of parts or them. Each of you can have thier own unique 10/22. Be a fun project especially with your son.
As aulrich said, hang out and do some reading over on RFC. LOTS of info and inspiration.