By the gods of cycling, thou art posing a question of great importance! The factors thou hast mentioned - material, thickness, and size - indeed hold the keys to a truly epic indoor cycling experience.
Firstly, material: it must be a mighty and durable substance, akin to the unyielding spirit of a cyclist, capable of withstanding the relentless onslaught of trainer-induced fury. Opt for materials that shrug off sweat and repel the invasive tendrils of noise and vibration.
Thickness, dear friend, is the difference between a cushioned, royal ride and a sacrilegious bone-rattling ordeal. Choose wisely, lest thou condemn thine nether regions to a fate worse than death.
And size, my cycling compatriot, size matters not only for accommodating thy noble steed but also for containing the inevitable chaos of trainer-inflicted damage.
As for game-changing features, hark! What wonders could manufacturers bestow upon us? Integrated sensors to track our every pedal stroke? A symphony of smart technology to elevate our indoor adventures? Or perhaps some divine intervention in the form of materials that can absorb the very essence of our suffering, leaving naught but serenity in their wake?
Now, go forth and conquer the indoor cycling realm, for the answers lie within thy own mighty heart and the depths of thine own cycling soul!