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