The key to telling the new no-GC Wiis from the old backwards compatible Wiis is the writing on the front of the system.
Because the old Wiis were designed to be placed vertically, all the writing is aligned appropriately. The word Wii is a the bottom, Power and Reset are below their respective buttons, and Eject is above its button. If you find these in the box (not likely at this point) they should picture the Wii standing vertically (my launch Wii box only depicts this on one side, while the other side shows only a hand holding the sleeveless Wii Remote).
The newer Wiis do not even come with a stand, so all the writing is designed for the horizontal orientation. Power, Reset, and Eject are above their buttons, while "Wii" has been moved to the left of the reset button.
At this point, the backwards compatible Wii has been out of production for quite a long time. Unless you happen upon a store that for some reason has a back stock of the things from at least last year, you will not find these new.
The vetical/horizontal thing is the key thing to look for when shopping for a used Wii.
And yes, a used, vertical-style Wii and component cables is probably the best way to go for Gamecube games, only lacking GBPlayer support... And with some software modding you can put GBA (and other) emulators onto one fairly easily, anyway.