The usual order for filter media in order of flow through your filter is mechanical, then biological, then chemical. There may be particular instances where a different flow order is beneficial or you may have a different personal preference, but mechanical, biological then chemical is tried and tested and generally this works.
Mechanical filter media is primarily there to filter out detritus from the water and is usually layers of sponge and floss. Sponges will also act as very good biological media. If you have more than one layer of sponge then you start with courser sponge to remove the bigger stuff, then less course sponge to remove smaller stuff, then floss to remove the really fine particles. Mechanical media will need periodically rinsing out otherwise it gets clogged up and flow will reduce flow through the filter. Every 1 or 2 months rinse it out using either water taken from your tank or tap water treated with a water conditioner. Don’t over rinse, you don’t need to get them spotless as the sponges will contain good beneficial bacteria and over cleaning could cause some loss of your cycle. For the same reason you don’t want to over clean your sponges, you don’t want to replace them unless you need to. Unless your sponges are falling apart and no longer functioning to remove detritus from the water you shouldn’t replace them. They will last years if properly maintained. The exception to this is floss. You might be able rinse out floss a time or two but generally just replace it whenever you do your periodic filter maintenance.
Biological media is where your beneficial bacteria lives. This is basically anything that has surface area for the bacteria to live on. There are generic ceramic rings, lava rock, branded products like Fluval Biomax, Seachem Matrix, Biohome, sponges, and more specialised media like K1. Plastic pot scrubbers work very well as biological media. What you are looking for is something hard wearing that wont crumble to dust in a short period of time because you don’t want to be replacing biological media. You also want something that will let water flow through and around it as it passes through your filter. Some media will make claims that its porosity gives it extra surface area as water can flow through the inside of the media and this inner surface area can establish anaerobic nitrifying bacteria that will consume nitrate as well as the ammonia and nitrite more normally removed by the nitrogen cycle. I’m not going to get into whether these claims are valid, but Matrix and Biohome are examples of these porous types of media. Biological media should last years if not decades. Maintenance wise, every month or two a light rinsing to remove any detritus is all that’s needed. Either rinse with water taken from your tank or use dechlorinated tank water.
Chemical media is commonly used to deal with specific issues in your tank. There are various chemical media products and they have specific functions. Generally chemical media is used to deal with a specific short term issue and then is no longer needed. Its expensive, needs replacing frequently, and once its done its job is no longer needed.
The most commonly used chemical media would be activated carbon. This will remove organic compounds and some metals from the water. These organic compounds can be tannins from driftwood which cause tea like colour in the water, so carbon is often used in new tanks to get the water clear until the tannins have leached out. Organic compounds can cause odours so carbon is used to remove these odours. After a course of medication you want to remove the medication from the tank and carbon will do this. Some people will advocate running carbon permanently, if you do this it needs replacing every 2 to 4 weeks as it gets used up quickly, so it becomes expensive to keep it as a permanent part of your filtration and you probably don’t need it.
Seachem Purigen is an alternative to carbon. It essentially does the same job, is more expensive, but has the benefit of being rechargeable, so instead of throwing away and replacing, there is a process where it can be recharged and reused time and again.
There are filter pads that remove many of the waste products your tank produces. Ammonia reducing media, nitrate reducing media, phosphate reducing media. The only sure-fire way to remove waste from your water is through the nitrogen cycle and your water changes. If you are cycled and keep up with your water changes the need to use chemical media should be a very rare occurrence.