Okay, so I followed your convenient tutorial for setting up the HBC with some success. I prepared my SD card, rented LEGO Indiana Jones, did the whole trick. I installed the HBC and installed BootMii as an IOS. At least I think I did. Now the HBC works perfectly fine, with emulators and everything. But when I press the home button and select 'Launch BootMii', the screen goes black and my drive's slot flashes in blue until the end of time.
I've checked my SD card, and it has a BootMii folder that is empty. I checked the installer.log files, which ends in the comment:

Quote
wii
BootMii: Can only be installed as an IOS
 The installed boot1 version prevents a boot2 install (-2)
..............................................

What am I doing wrong and how do I fix this?
Thanks for your help.

run the HBC installer again, but when you go to the bootmii part, make sure you hit prepare SD card. This will place the necessary files on you SD card to run bootmii.

Thanks, I'll try this later on. Are you sure this is the right way, though? I'm confused about the boot1 version thingy…

Look at this Bootmii

You cannot install BootMii as boot2 because your Wii is new enough that boot1 will reject it.

You currently cannot run BootMii as IOS because the majority of it is supposed to be on your SD card, which it is not. The solution is to let the HackMii installer place the necessary files on your SD card so that BootMii can run.

Okay, I redid the whole thing, and now I'm able to launch BootMii. Still a bit confused and I can't quite figure out how to play my backups…
Either way, thanks a lot for your help! You guys are great.

Read the rules. NO BACKUPS. And BootMii has NOTHING to do with that anyway.