Sounds okay from here but then it is something that you can look over and see how it might work better. Three gallon with a single betta? That says not much bio-load. So most any sponge or soft media will collect enough bacteria to handle the load. Sometimes more media to slow the flow, sometimes less to get more flow? I would watch the flow and how clean it is getting the water. Finer media like filter floss pads are good for the mechanical straining. I would suggest one that can be rinsed and reused a number of times before falling apart.
In general the idea is to run the water through one or more mechanical "strainers" and then if you want bio filtering which is prone to getting the little pores stopped up, add it after the mechanical. Then if you want to "polish" the water, a layer of really fine stuff. Not all situations require all those, so it may need some watching and small changes as you see how it works for you and the big guy.
Thanks, I have never tried anything beyond what I have learned from using an Aquaclear 70. In my Evolve 4, the media chamber is exactly the same size as an Aquaclear 70. So what I did for that was put a sponge at the bottom, a carbon insert, and then another sponge, and then the biorings. All from basically what would be put in an Aquaclear 70. I know the double sponge is a little over kill, and all of it barely looks dirty even after a year, again probably because of the bioload being so small.
But I took the same principals from that and applied it to my Tertra Whisper. Originally when I started with nano tanks with built in filters, I never thought I would even be able to understand how to find a replacement to the cartridges. I have to say, the water in my Evolve 4 is crystal clear.
The flow in my 3 gallon with the Tetra Whisper is a little less than what ideally I wanted. But then again Bettas do not much care for flow. The water looks good though. I will be testing the water every few days to make sure I have not caused any issues. I am leaving the old cartridge in the tank for a few days to make sure I get all the beneficial bacteria I can.