I would run them seperately.
Ok so you will have to clean the one with filter material more often, the other one would hardly ever need a clean at all. I would add a layer of coarse foam to the bio media one just to catch particles that may get caught in the propeller.
As for media, well matrix, purigen, calcium carbonate or similar, rough ceramic noodles, these seem better to the smooth ones.
I tend not to use filter wool, clogs up to easy, & the water ends up running around the edges of the material. I tend to use a couple of different types of foam sheets. Coarse & not so coarse.
That is why I tend to use the cannister as bio load with coarse foam{which the bacteria grows on too} & use an internal with finer foam to collect all the smaller particles.
Frenchy