What would a mat do for my Garrard 301 turntable

I see that there are many different mats for sale for turntables.

* I am wondering what do they do sonically ?

Also any suggestions on what mat works best for this Garrard 301
Hit your bare platter. If it rings then a mat would probably help. The Garrard was designed before it was understood that the very low level vibrations from playback could have an effect on the sound. You should get better record isolation with the right mat. I use to sell several but that was long ago. Look on Vinyl Engine and HIFI Wigwam as they are more likely to have experience with the Garrard.
here is some good read for you :
The Garrard 301 and 401 and the Lencos need a heavy mat to damp out ringing in the platter. The stock Garrard mats do this well. I've had good results with using a Spotmat on top of the stock Garrard mat. But the Garrard mat...or some other heavy alternative to damp out the platter resonance...is still needed.
I recently ordered a "Custom Design (Company) Inert Turntable Matt", made in the UK. It's in transit.

It's supposed to work well with "ringing" metal platters, such as my Dual TT has. Better than the stock rubber mat?

Dunno yet.