the WW1 Gew98 was speced to have Walnut, but mid-way through the war walnut became scarce and unlaminated beech came into use. After WW1, production reverted to Walnut only. Most refurbed G98's made into K98b's were walnut stocked - I've never seen one that got to keep beech (though they undoubtedly exist) so i would say it was regarded as a secondary choice.
Prior to WW2, Walnut was the sole wood in use for the Gewerh fur Deutche Reichspost, the Standard Modell and the K98k. Once production really stepped up in 1940 or so (because a war was on!), the Germans developped the Laminate stock to make use of the vast stands of beech trees in Germany at the time. This allowed beech to be as rigid and warp-resistant as the European Walnut they were using before, though laminated beech is marginally heavier. Walnut was still used throughout production as it became available, but the long kiln times to season walnut meant that it could not be sourced quickly enough to satisfy the reich's demands for small arms production. this is why the majority of war time rifles are found with the laminate beech stocks.
There are also two different types of laminate commonly encountered. The early type with red adhesive (glue) and the later type with white water-based glue (a wartime expedient due to allied bombing efforts to hinder German adhesive production).
The Germans also made limited numbers of bakelite stocks for their K98k's, though they are VERY rare today.