Hello Bill, welcome to the forum.
If you have a good tight stove with good gaskets on the doors, and air controls that allow you to just about shut off the air to the fire, then there really is no need for any damper at all. Notice I said need. The stove will function just fine without one.
The Baro damper will be a help in controlling the burn during windy and changing weather conditions. Without a baro damper, when you have the stove set for normal and calm winds, to give a certain burn rate and heat output for the day or night. Then if the weather gets cold and windy, the added draft from the chimney will pull more air through the fire, burning the coal faster, and most of the extra heat will go up the chimney.
The baro will 'break' the strong draft, the flapper door will open and pull air from the room, instead of from the stove. This keeps the draft over the fire the same, so the burn rate and heat output will be much more consistant.
As for the hand damper, it is a leftover from the days of pot-bellied stoves and Franklin fireplaces that had very little control of the air getting to the fire, so the hand damper cut back the draft when the stove was set to burn, and the damper could be opened when loading more fuel on the fire to keep smoke out of the room.
I personally see no reason for both types of dampers on the same flue pipe. But I'm open for ideas and getting an education.
I'm sure there are instances where both are desired, maybe some of the other forum members can post their comments about using both dampers together.