Looking at the front of your house i d do at least a 5 12 up to a 7 12 roof pitch and gable it.
Hip roof with gable addition.
Hip roofs are more expensive to build than a gable roof.
In my opinion roof pitches with gables that are less than 5 12 don t look nearly as nice.
Also known as a pyramid.
You d probably end up with some cricket areas where the gables meet.
If you gabled the roof instead of having a hipped one it would give it more prominence.
Gable roof addition to hip roof house in order to have the existing roof line plane through you ll need to match the pitch from the existing to the new addition.
For high wind areas or strong storms a pitch of 4 12 6 12 18 5 26 5 angle is recommended.
It s a more complex design that requires more building materials.
It may be better to stick frame the addition roof.
Gambrel roof a multi sided.