the softmod process itself got way easier than half a year ago.
a black wii has a dvd drivechipset which can't run any burned dvd. a modchip won't help with that. (only hardmod solution would be a wode where you attach a hdd to, softmodding is for free..)
get a usb hdd. use the softmod any wii guide linked below and the fat32 loading guide to prepare the hdd and your game collection.