Well, the Wii is very modular, so you could take an equally modular, piece by piece approach (1) or the nuclear approach (2)...
1:
a bunch of random stuffy homebrew and menu themes.
1b: removing themes has been discussed today in
https://gbatemp.net/threads/help-i-installed-a-custom-theme-as-a-wad-and-i-cannot-borrow-it.673398/ , basically you can just reinstall the wii menu or install the official theme over the current one
1a: most homebrew is not "installed", take out any SD and USB to see what I mean;
any save/channel can be removed in the official settings*
(this is not very clean in that it will leave a ticket, but it will be irrelevant for most practical purposes, and even if removing the ticket - eg by uninstalling them with AnyTitleDeleter Bushing Mod - there will still be a trace in uid.sys unless you use method (2) but this too won't affect future use) but I would keep the HBC as it's the most convenient entrypoint after all;
custom system titles will remain installed but won't be a big deal because... see below
* the official "factory reset" doesn't do much more than this, except possibly to screw with the Wii Menu if you have Priiloader installed (easily fixable, mind you)
2:
create a nand backup, use Ohneschwanzenegger to create a new clean install system image, and flash the new "backup" back - extremely effective and clean but it's annoying and relatively risky to restore a backup if your Wii, like most, doesn't support BootMii as boot2
After doing either (or a number of other intermediate approaches, or neither):
You can "clean up" your SD/USB (absolutely nothing is required for normal operation) and then use ModMii to download and install modern "core mods" (HBC, CIOS, Priiloader, ...) and clean up the system titles - this will largely be an "overwrite entire titles" approach, completing the job in (1) if you went that way
