Any platter designed correctly will not resonate regardless of what it is made from.
A well designed mat has the mechanical impedance of vinyl and has relief for both the label and the edge of the record. Any floppy soft mat is bad. But, just as important is the way the record is clamped down. Vacuum clamping IMHO is the best followed by reflex clamping of which the Sota Reflex clamp is an example. SME and Kuzma do it by having a clamp that screws onto a threaded spindle.
A properly designed suspended (isolated) turntable is always best. Examples are SME, the Stabi M and Ref 2, Basis, Sota, Avid and Dohmann. I personally prefer belt drive. It can be just as accurate as DD. Isolation and proper record clamping are more important from a sonic perspective as long as the drive is executed correctly.