You can use betwiin to convert a NAND dump from one wii to work with another wii, but I'm not sure if VC and WW titles will work perfectly or not. Same for save games.
However, you will
not be able to install BootMii/boot2 on the new Wii. Only BootMii/IOS. You
can restore a NAND dump with BootMii/IOS, but it is a more "dangerous" procedure because if something goes wrong, you don't have BootMii to fall back on.
With BootMii/boot2, if something goes wrong while restoring a NAND dump, you can just restart and try again. With BootMii/IOS, it's sort of a "one shot" deal. If it doesn't work out good, you will have to pay someone to reprogram your NAND (unless you happen to own a NAND reprogrammer [e.g. Infectus] and have the knowledge/skills required to use it).
For savegames, you can use a tool like Savegame Manager GX to backup all your saves from one Wii and install them onto the other. But that won't work for VC and WW games, just for your savegames. (This does NOT require restoring a NAND dump, so you can easily do this without BootMii/boot2.)