I looked into this topic a lot these past few weeks.
I think either Matrix or Biomax would work nice. Matrix is good because it's pumice which is the most porous rock on earth which means it's a natural stone with a ridiculous amount of surface area through out. it'll be harder to kill all the bacteria colonies when doing rinsing although they can "clog" a little easier than biomax. Biomax is great because it does both mechanical filtration and bio filtration because of its ring shape while still being porous but it can be reset a little easier when rinsing it. The combination though I would think though would be very good and not overly expensive simply because matrix has a strong biofiltration and biomax doubles as both so not to waste any space. You can put the biomax in bottom chamber and matrix in top chamber, under polishing pads. I think putting polishing pads on bottom and on very top with media on top or underneath it in the same chamber is good to keep the media free from particles and also to polish the water overall.
Purigen could work instead of carbon too and you can save the carbon for when you want to remove medications or something since purigen last longer and is renewable and I think almost everyone that uses it holds it in very high regards. It won't remove good things in the tank either just organic waste and tannins
These three things aren't as expensive as other options and do very well.