I think the very first thing you need to decide in selecting a mat, is what you are trying to achieve. There are probably two basic schools of thought.
1. One is to isolate the turntable from the vinyl.
2. The other is to solidly couple the vinyl to the turntable.
They are two very different approaches requiring totally different mats. You would choose option 1 if you think the vinyl has enough mass and is stable enough under cartridge tracking force to essentially be immovable. It also has to resist moving as a result of sound waves. The isolation method attenuates the rumble from the table.
At the opposite end of the scale you have the solidly couple method. You would select this approach if you are concerned that cartridge tracking force or sound waves from a powerful system will cause your vinyl to resonate. Attaching it firmly to the heavy TT platter will significantly attenuate induced vibration in the vinyl.
Could you do both? Yes probably if you had essentially two platters with a decoupling layer in between. The top layer would have to be heavy and firmly attached to the vinyl, and the two layers would have to be free to vibrate independently, with the bottom one responding to rumble, and the top one to self resonance.
I would suggest the no mat at all option is a #1, in that the vinyl is free to move and vibrate as it will never fit perfectly flat on a hard surface. A cork mat has very little mass or adhesion, and again is a type 1. A felt mat is probably the same, but there may be some slight damping from the felt. If you believe the vinyl resonates, then this resonance will obviously color the frequency response.
In the other category you have the tacky adhesive mats, sometimes enhanced with a clamp above the vinyl. This is for the believers in the vinyl resonance, and confident their TT rumble is very low. I'm a Type 2 supporter, and like the adhesive mats. I want the vinyl to fully couple to the heavy mass of the turntable platter. That way the influence of sound waves and cartridge force is highly attenuated.
There may be a bit of an in between approach, which I have not tried, but may do so. My wife bought some cupboard shelf liner material in a roll. It is slightly tacky fake coarse weave material made of a high damping type of foam plastic. When you compress it, the rebound is very slow. My guess is that it could be far superior to felt and cork. It will provide some damping and some adhesion.
In the end remember it is all about reducing resonance vibration of the vinyl and isolation from rumble. I suspect resonance is the main effect heard by changing mats. If listeners like the coloring of the sound caused by the resonance they like the mat. If there is no resonance the frequency response is more true, but lacks that colored appeal. i.e. the best mat from a technical point of view, may not please listeners the most...
Here is a link to the shelf liner material. By the way, I think it is useless as a shelf liner. Because it has a grippy surface it wrinkles up and is hard to smooth out. Also dishes refuse to slide on it. I think they should start selling it as turntable mat material instead!!http://www.stacksandstacks.com/shelf-liner-grip-it