TYRES
Mtb tyres
Mtb tyre i think are the easier one were the didnt improved so much in the last time,,other than specific and rare cases i would use 2.35/2.4 tyres so u can run lower pressure(by having bigger volume) and having a larger thread, the casing should be sturdy but lightweight, personally on xc a tire heavier than 700g i dont like it but on these harder course that we see today its not that bad, i personally use specialized fast trak control(i could use the lighter s-works on the front but i think its too supple that could be a good thing but depends) 2.35 on the front and renegade control 2.35 on the back, if i remember well with 60ml of stans no tubes sealant for each tyre (i have the weight of each tyre written at home so im gonna update it here but its different in every tire so dont count too much on it) thinner tyres for real mud are better even 2.0 because they sort of cut through the mud
Cyclocross
Here the things get more interesting, the tyre choice is more important, but keep in mind you should have at least 2 wheelsets the first with tubeless or tube for training and the second with tubulars (this should be race only, ofc if u want to waste money or pro you can do what u want),first what are tubulars, they are basically tires that are glued to tge rim im gonna post after this message how to glue them everyone has his method but i say what works for me
Why tubs are superior? Basically you can run them at lower pressures without having troubles, another extra is that crazy suppleness because the sides on good quality one are made out of fabric rolling resistance and weight arent so important here because being on the bike its more valuable than some saved watt if someone had only 2 types of wheels (tubeless and tubular) i would put medium terrain on tubeless wheels and on tubular wheels mud tyres simply because the tubular shine more on mud
ROAD
On road its pretty easy tubeless is superion in literally everything and i think 28mm its ideal now if u are interested go on this site to find the fastest tyre Bicycle Rolling Resistance | Rolling Resistance Tests
Remember confort its also efficiency and wide mean safer/faster in downhill
Tubs are interesting only for weight and its not huge
Im gonna continue with the hardest that its gravel next