Last I played, there is no option that changes the default fire mode of a weapon when you pick it up off the ground.
I believe that if you pick up a weapon from dead persons loot box or a weapon that someone dropped, it will be in whatever fire mode that they were using it in last before they died/dropped the weapon. These are the only exception to this. You will have to simply remember to switch the fire mode upon picking a weapon up.
With the Update #25 Patch, there is now a game option to set the default weapon fire mode of guns. Reading the patch notes for the update:
Added an option to set default firing mode for weapons
This patch is currently only on the test servers, and should be expected to be released onto the live servers sometime in the near future.