Cork, felt, rubber, Sorbothane, glass fiber, leather... It's a matter of taste (and when DIYing also a matter of availability/skills/appropriate tools).
Keep in mind that with many turntables the thickness and weight of the original mat was part of the design. In other words: the thick rubber slab on a 1970s Japanese direct drive deck was probably there for a reason. Same goes for subchassis decks like the Thorens 160, 320, 2001 families: reducing the suspended mass will change the tuning (resonance frequency) and effectiveness of the subchassis.
For a thin mat, I'd probably start with wool felt which works really well with a lot of turntables. However, ready made felt mats are so cheap that it's probably not worth the trouble making it yourself.
I was told that, due to me having a metal platter (just a typical direct drive turntable like the Technics SL1200), rubber is best.
Actually, the decks came with two different mats. A rubber one and a thinner (looks like felt/cork) item with a very thin separate layer of plastic underneath. If I remember correctly, even Technics was recommending using the latter in tandem and not using the former at all.
However, this might have had to do with scratching and the lot. Not sure about the reasons anymore.