How do I update without losing the Homebrew Channel?

I want to use the internet on the Wii

You mean updating to system menu 4.2? It only deletes the title that have the id HAXX, used by Homebrew Channel 1.0.4 and lower. If you update HBC to 1.0.5 or higher, it won't be deleted by the system menu upgrade.

You can also use the Internet without updating

Quote
bg4545
You can also use the Internet without updating

He cannot download the Internet Channel from the Shop Channel unless the Shop Channel is up to date...

I wasn't talking about the channel, but yeah he could update only the shop
channel to get it.

Or he could install an internet channel WAD, which can be obtained with NUS Downloader.

In my very little experience, i;ve a wii 4.2U with HBC, and I run into the same problem.
I just put DOP-IOS, enable internet in the wii, and install the internet channel with DOP-IOS and work great.

with internet installed and Wiiconnect24 disabled ( to prevent unwanted upgrades ) DOP-IOS will download the channels from NUS, so no need to prepare anything.

I also upgrade the shop channel ( i was courious about all those shiny things nintendo offer there )

BTW if you allready have the 4.2U you dont need to upgrde any other IOS , I just run systemcheck with DOP-IOS and check the versions of all the IOS installed and compare with the lastest version in the wiibre.org. IOS61 seams to be updated to the last version, so i just install the shop channel.