It seems like the store is where you will get the most and the most quickly. You get some pieces in WoL, but that will take a long time to get through. You can pick up costume pieces (and other things) from Classic mode rewards, but that also is time consuming and you won't get more than one piece per play through. In the store, I've bought up a lot of the songs already, and once you get more slots in the store, it seems like I have 3+ Mii costume pieces waiting for me every time the store refills. You will obviously need to acquire gold to pay for them, but that's not a big problem...
It's unclear whether you have to play WoL (or beat challenges) to get every Mii costume piece though. But the large majority of pieces seem to be available in the store.
