The sponge thing, leave it alone. That will keep debris from getting into your return pump. You do have to rinse it out when you do water changes though or nitrates will build up in it.
The bioballs are a big thing, you have to decide if you want to ditch them or keep them. If you get rid of them then I would get something like this
Coralife Biocube 29 Media Basket
The basket will let you run whatever you want in it, carbon, gfo
(for phosphates) or other stuff.
The bioballs can trap debris and build up nitrates. I used the basket and liked it very much. Its $50 but worth every penny
They also have a fuge basket you can buy at that site too, you can keep macro algae in it and that helps reduce nitrates.
Not sure what you mean by "coral" thing.....the far right compartment I used to keep my heater in. You wont need the filter cartridge either if you go with that rack i just linked.