I also make my own and have tried several styles from AIO's to fitted and full surround pullups to waterproof pants with snap in inserts.
For myself, being UK based mostly I will use Terry towel for absorbent layers as that is what is available, There are other options easily available here like fleece, sherpa, velour, french terry etc. but not many places selling Birdseye in the UK and gauze seems more expensive.
I also used Microfleece as the inner liner for wicking, dry feel and easy cleaning but I am slowly switching to
athletic wicking jersey (has several names) which does the job slightly better but stains so easily. I also use PUL as covers/outers as I don't really like PVC or nylon.
As for what you can use in a diaper there are so many options.
Fabric fibre wise there is:
Microfibre, Cotton, Bamboo, Hemp and Zorb. They all have different speeds and capacities for absorption here is a handy little chart to compare them.
Microfibre: is commonly used in baby diapers as it is very cheap, easy to clean, fast to dry and does its job well, but not against the skin as it can draw moisture from the skin and cause dryness. It can work and be effective for adults but it may not have the capacity for a heavy wetting adult especially under compression. Babies are much lighter and do not pee as much so the lower capacity and compression is fine but MF suffers from compression leaks (average about 44% lost from max after compression). It generally comes as a Terrycloth so is quite bulky, it makes for good top layers on the absorbent pad section where you need it to suck up pee fast.
Cotton: Is also commonly used, it holds a bit more than MF at max and holds it better under compression (around 28% loss from max on my tests) it is also fairly cheap. you can get it as Terrycloth witch is effective but thick, Sherpa which is like an even thicker Terry, very effective and soft but very bulky, Velour which is nice and soft and quite thin, Gauze/twill/birdseye which is pretty much the American standard smooth feeling and effective or Fleece which is thin and soft. Cotton fabrics can also make a good top layer, they are not as fast as MF but are fine against the skin. Cotton does tend to feel very stiff or a little rough after washing (especially terry), This can be helped by tumble drying a little or rubbing and vigorously shaking when dry.
Bamboo: Is a newer fabric in diapers, Like cotton it comes in the same finishes but is quite slow and somewhat expensive it does however have a higher max capacity and holds really well under compression (loss of around 9% from max), it is luxuriously soft and gets softer with each wash no stiff felling to it. Many cloth diaper makers will use Bamboo Fleece in their diapers I'm yet to fully test it but fleece and Terry should have similar hold and speed but fleece is thinner, less bulk means more layers for higher capacity. Bamboo is not an overly strong fabric so often comes blended with poly or cotton to strengthen it.
Hemp: Is the god tier for max capacity and compression hold, I don't have figure as I've never used it to test but this stuff can legit hold a lot, it is the most expensive though and it also suffers from rougher and stiff feeling after washes, it is also prone to holding odours. Usually found as some kind of weave (gauze/twill), it is excellent for bottom layers of the absorbent section (furthest from skin but sill inside the outer layer).
Zorb: Is the outlier in that it is both Very fast and Very absorbent (up to 10 times it's weight) but due to it's mix of fibres doesn't really hold in the same way more like it traps moisture between fibres than soaking them into fibres. It comes in a few forms: Zorb 1 is like a felt and needs to be sandwiched between other fabrics or it will fall apart, Zorb 2 (3d) comes pre-sandwiched between either cotton or bamboo, Zorb 3 (4d) is pre-sandwiched and also has a PUL layer already. This stuff is quite trim but a little stiff when sandwiched cleans easy and dries fast but is best used between layers of better holding fabric like Bamboo or Hemp due to it's higher compression leaks.
Most of the fibres can be found in different fabric finishes (Terry, Fleece, Gauze etc.) which can affect how well they work to a degree but also affect their bulkiness, less bulky fabrics may not hold quite as much per sq. inch but you can use more layers to get the same thickness as a bulkier fabric for more capacity overall. It mostly is about what finish you prefer and which you can get easiest.
A rough thickness guide from trimmest to bulkiest:
Gauze/twill>fleece/Velour>French Terry>Terry>Sherpa
You will also want to take smells into account, MF cleans well and doesn't hold much odour, same with bamboo little to no lingering smells, Cotton can hold odours a bit more and hemp can get quite smelly. In order of least to most I would say it is probably Zorb>bamboo>MF>Cotton>Hemp.
Depending on the type of Diaper you want to make will affect which you might want to choose, for example if you are making an AIO or a fitted that is going to wrap all around will have larger areas for absorbency, thinner and lower capacity fabrics like cotton and MF are fine as there will be more of them overall to make it up but for a pocket diaper or anything that uses a straight insert/pad as its main absorbency will need the higher capacity and faster fabrics to catch pee quickly and hold on to it.
Then there is Layering to consider, if you plan on using separate waterproof pants the outer layer of the diaper can be practically anything, most use flannel, brushed cotton or fleece for a nice soft feel and look. The absorbent part should have slower but better compression holding fabrics on the bottom (outside) and faster fabrics on top (near body) so for instance Bamboo terry/fleece then MF on top. Zorb is the odd one out in that although it has high capacity and high speed it also has high compression loss so need to be in the middle of a pad.
The inner layer has a few options to choose from some like suede cloth, some microfleece, there is also minky, your coolmax might be ok and Athletic wicking jersey. I personally always used Microfleece, it's very easy to shake and messes off cleans well, dries fast and does feel dry against the skin I do however notice that the liners I made do tend to make my skin a little itchy and sore if I sit in a wet diaper for too long. I have started using the athletic mesh which is Crazy thin does a really good job at feeling dry until diaper is over saturated and has not caused any itchiness yet but stains way to easily (get a darker colour).
Hope some of this helps, let us know how it goes it can be a lot of fun making your own and exploring different options.