Softly, Softly.

The idea of a layout is to run trains.

I dislike the noise usually assocated with model trains, - the incessant din that drums through the plywood baseboard, and becomes an overbearing racket.
I have been exposed to this unpleasant experience at model train shows for often days at a time. All I wish to hear is the swishing sound of wheels on rail, and the clickety-clack of the rail joints.

On my layout I use Marklin C track, which has a built-in plastic ballast. Firstly I do not screw down any track and the layout has been working now since 2007 without track problems.
The use of screws actually transmits any track noise directly to the ply-wood base and thence to any wood framing. You can imagine this acts like a largish violin or guitar.
The noise of the electric motor and of wheels on rail is amplified through the screws to the timbers.

I think I have created the ideal sound deadening 3 layer system under the track but you might be satisfied with only one of the layers.

1st layer - a vinyl or core-flute underlay (available from a flooring shop, or even given away by hardware shops if it comes sandwiched between block layers).
This might also be a woollen or similar underlay often used for flooring.

2nd layer - a Noch underlay paper product (60840), of which I cannot speak too highly - see pictures and explnation below.

3rd and final layer under the track bed - a landscape roll (ballast, grass etc available from Woodland Scenics, Noch, Busch etc) that go directly under the track.

The Noch underlay is a coat of tar or similar substance, sandwiched between two sheets of crinkly heavy paper.
It is brilliant, and certainly deadens a lot of track based noise which is normally transmitted to the baseboard. I also use this paper in other areas for landscaping, because it can be readily shaped over any sort of former.