I've put "displaying" in the vote, but as my son and I share the Playmobil (and my husband has an occasional passing interest) it's more a case of "play and display".
The boy usually sets up a display on the floor, with a running commentary as to what is going to happen, and then we either play together, or I watch and listen, as a story unfolds. If I had more time, I'd record the lot as he has some fabulous ideas. Likewise, I should get the camera out more.
As for customising, he often swaps hair and hats around to suit the purpose of a story or to make one of his people look like someone he knows. He also improvises if he hasn't got something he needs, he'll use something else (also a subtle hint to me as to what's next on the shopping list!!). We also mix and match most of our sets to suit what's going on in his "Playmobil world".
We've done a couple of stop motion animations too, and again, it's more a case of time (or lack of it) that we haven't done any more. There are several in the pipeline (or rather in my son's head).
So, it's almost "all of the above" really, as everything starts with a display. When our builder has finished moving the walls outwards (
) we'll have space to have a display going while we are playing with the other stuff. I'll be able to get the secret stash of Playmobil out of the loft then (bit by bit, of course)
and you can see what else we've got (although you haven't seen everything yet anyway as it's a bit too chaotic here, and I've been a bit too busy to keep on top of the photography of late).