I highly highly and once again highly recommend you outflow be much larger then your inflow. The last thing you want is to have the water coming in faster then It can flow out, also with the outflow like you have in you picture you will get reduced flow rate so you will need to use even larger piping. 1" piping plumbed like you show will probably flow like 250gph to 350gph for your outflow.
I only have a 220 gallon with 55 gallon sump, I push about 600 to 700gph and have zero problems. Some people will tell you 10x Turn over some people will say 5c turn over, I think 2x to 3x will work fine. You can always increase it with larger pump or power heads provided your outflow can handle it.
as far as the matrix goes you can use bubble bars or a power head in the container to increase circulation, but alot of people just have a bag of bio rings in the sump, its more about contact time then how much flows through it. It works like osmosis, the water gets cleaned by the bio, which dilutes the rest of the water, this keeps happening till nothing is left.