Totally your choice on what you do with the boxes as they are yours.
I cut all the unnecessary stuff off of the smaller boxes. For Siege/ER, I remove and recycle by cutting the seam below and above the name. This keeps the character art and back panel. I trim those and recycle the small bits with the whole front and plastic. For the MMs or BMs, I exacto and then recycle the plastic and toss the cardboard piece since it is generic.
I will keep the boxes for someone bigger like Jetfire or Omega and since those have the nice shared art sides, I don't need 20 copies of those from the Deluxes, Voyagers, etc.
All the cut pieces that I keep are stored flat in a smallish sized box.