Update first and HBC then or vice versa?

Yesterday I got my brand new Wii. Well, obviously is not that brand new, because it has system menu 3.4E. This means I do not have SDHC support.
So my question is: should I update to a newer system menu now and install homebrew then or vice versa?

Either way will work.

seeing as its 3.4, if you happen to have twilight princess, i'd use twilight hack to install HBC first, then update. It's more reliable than bannerbomb. however, if you dont have twilight princess, you can do either. But my advice would be try bannerbomb on 3.4, that way, if none of them work, you could rent/borrow/buy a copy of twilight princess and use twilight hack.