Except for one case, Collectibles serve no purpose except for achievements. To earn the related achievement, you must find the required amount of collectibles during a single match.
In the first Killing Floor, you must find all the collectibles on the map in a single run. On Moon Base instead of destroying the collectibles you have to press the Use button to pick up all sixteen pieces of the Zed Eradication Device. This will unlock the weapon for purchase at the Trader.
In Killing Floor 2, you usually only need to collect ten collectibles, though the map may have up to thirty or more. During Early Access there was a period that required you to collect all thirty collectibles, but it was reduced to ten. Early maps all use the Dosh Medallion as their collectible, but later maps begin to vary it up some.