I love stuffing those boxes! I've probably stuffed four or five of those boxes in my Disney shopping career. Here is my Potato Head Part Stuffing 101:
The trickiest thing are the extra big parts, like the Buzz Lightyear ride vehicle base, Aerial base, etc. Always start with the biggest pieces first, then go smaller.
Avoid standard pieces you can buy at a non-
Disney store.
Check any Character Warehouse stores, I've found many of the Disney parts there for 25 cents each! (At WDW this is the store in the nearby outlet mall. At DL, the nearest permanent store is in Fullerton - about a 10 minute drive from the park).
If a piece has any "pockets," (i.e. inside hats, under the bases) stuff those pockets with one of the small items. (Mickey Bars are my personal favorite, you don't even need a potato head to love those. They work with dolls, beanies, gift package toppers, you name it!)
Look at your box as several layers. Put your first big piece in the bottom, fill around it, then put in your next big piece.
You must be able to close the lid. Don't be shy about stuffing the box so full that the sides of the box are bulging out.
Some parts seem to be only available at certain parks. The best selection I've seen is at the Once-Upon-A-Toy store in Downtown Disney. Start there.
If you find one piece in a park that you couldn't find anywhere else, ask a CM nicely if you need to buy a whole box for just that one piece, or if you can buy it separately instead. Many times they will let you have the piece, depending on their mood and yours.
Check for any of the packages of parts that are sold separately. There are some that can be bought through
Amazon or other places (they are called "Spud Parts & Pieces) it's almost always a better deal to buy these on their own. The stuff a box for $20 is not much of a bargain, even after much creative, time-consuming stuffage.
Most of all, have fun! I have to take inventory of my pieces before my next trip. I know there are some new ones out there (different arms, etc.) so I'm really looking forward to my stuffing excursion!!