What colour to use on this part?

Go with the base color of the vehicle on the mesh. Panzer Gray, Dark Yellow, etc.

I know that this is the 37mm mount, but the vehicle chassis is the same.

It was (SFAIK) just metal mesh....

The viynil-like black mesh in the box doesn't hold paint well, so I would replace it with generic metal mesh,

Several PE vendors have this, & should be cheaper  than a model-kit specific PC, unless you want to of course!

Paint would be body-colour, probably Dunkel-gelb, + and camo as applied, and rust/weather to taste.

In reality the "mesh" walls were not a netting but actually a grating with perhaps 1" slats crossing one another.  A Japanese company has made an aftermarket part to fit the newer Dragon versions of the SdKfz 7/1 kits. 

http://www.kamizukuri.jp/FeerinngPart/imeges/sdkfzpart_l.jpg

http://www.kamizukuri.jp/FeerinngPart/index.html

With these parts, you see the 3-dimensionality of this grating versus the "flat" depictions of PE or mesh materials.

 But to your original question: the grating formed part of the extended work surface for the gunners when lowered.  It would have been painted just like the rest of the vehicle.

Thank you gentelmen. Stickpusher, those photos are great, gave me some ideas to do some damage on the wehicle.

Cheers...