The Wii Mii Channel has extremely limited customization. You cannot download new clothes/hats/accessories like on Wii U/3DS/Switch. The wardrobe is fixed at ~12 shirts, 6 pants, 6 hats, 3 glasses, 3 beards, 3 moles.
With Letterbomb / BlueBomb exploit + Priiloader, you can install Mii Editor homebrew to inject custom .mii files with any outfit. High effort, bricks if wrong.
Bottom Line: For variety, make Miis on Switch/Phone app → Transfer to Wii. For pure Wii, grind Wii Sports Pro ranks.