Sponges are the best filter media as fas as I'm concerned. they trap the gunk and hold beneficial filter bacteria. A layer of fine filter wool (Dacron) is also useful as it traps the very fine particles that sometimes pass through the sponges.
Ceramic beads/ noodles can be used but are mainly designed to hold filter bacteria and don't do much to trap or hold the gunk.
Carbon can be used if you like but it is mainly used for removing chemicals from the water. This will include medications and plant fertilisers. It should be replaced every month, if not more often. I prefer not to use carbon because it isn't really necessary unless you have lots of heavy metals (copper, etc) and chemicals in your water supply.