I'm using barrels in series like your first diagram, it's easier to define what you want each barrel to do. I'm only using two barrels, but have one large cone shaped tank I'm using a vortex settling chamber. This is my first year with it, but I'm finding the settling chamber is working quite well.
I have read that the nice thing about strapping material is it is easy to clean. You basically just stir it up and slosh it around every once in a while to remove the “dust” and it’s clean. It’s very light so complete removal is easy if need be, and has no deep pours or internal chambers where debris or gunk can get trapped like lava rock.
As for it not holding “bio film”, I guess there is some that might be better than others. I am using some Savio springflo strapping which they claim is impregnated with calcium and has a diamond grid surface texture on the surface to encourage bacteria growth. To tell you the truth, it looks just like many other similar sized strapping I have seen before, but who knows, right?
If I was to use lava rock material in a barrel I’d get it up high and set it up as a trickle type filter (not submerged) and make sure you had really good mechanical filtration before it so it doesn’t get gunked up too fast. Removing lava rock from a barrel to clean could be a real pain.