We usually use pine for door frames
I think is the cheapest wood to work because is gonna be painted
But you can always use any kind of wood . It depends on what kind of wood is your door. .I mean when it is gonna be varnished.
It depends on what you want and how long you want it to last. Cheaper wood's pine etc are fine but if you want quality go for a hardwood. Obviously the hardwood is more expensive.