This is an exploded view of a rafter foot and seat on a plate – a rafter seat housing.
Here you can see the plate with post below. And the rafter with a notch cut into the back side of the plate for the rafter foot to sit on. 
The toe of the rafter has been trimmed to the outside edge of the plate.
The location of the birds mouth cut on the rafter is important to prevent the rafter from splitting.
Care has to be taken to account for timber shrinkage when cutting this joint.
what is the best way to seat a 3×12 rafter on beam plate? is best to use a simple birds mouth as on traditional framing?
Yes, that is the simplest way to do it.