The first stoves were designed for existing chimneys or fireplaces. Many homes had parlor stoves vented into chimneys and certain configurations were needed to upgrade from less efficient stoves. People today still buy stoves for existing chimneys and don't realize they should find the stove made for their installation instead of making due with the incorrect configuration. You can't always find what you need with them getting rare in areas now.
They were available in side, rear or top vent. It doesn't seem the early ones were too common in top vent. (Bob probably discouraged top vents due to heat loss)
Side was the first configuration designed for setting across the blocked off fireplace hearth avoiding projecting the stove out into the room. They were available left or right side vent to position stove as needed. Door should open towards hearth face to be out of the way when open for easy loading. Hence the left and right hinged doors. (Pictured is a two piece top common to Washington - not sure how many others copied this design before going to one piece bent tops - could be Washington only. (Bob's cousin) Notice it should have a left hand hinged door in this left side configuration for hearth front installation. This one would be used for through the wall with chimney on the left side. (through the wall horizontal pipe should always use double wall pipe inside as well)
Rear vent for through the wall installation or good for low horizontal run into fireplace under mantle when the hearth pad is large enough projecting into room. (Shown with the original type elbow, correct for early 3 piece top)
Top vent for straight up venting under fabricated chimney, or setting in front of masonry chimney to allow closer clearance behind stove, or corner installation.
The vent pipe should protrude down into the stove from stove top to prevent excessive heat loss, but this style is still the most inefficient.
Adding an angled baffle takes away from the smaller firebox area of a Baby Bear, so you can fashion a flat plate under the outlet the same as designed on Honey Bears. (They were welded in, but you can drill 3 holes in the outlet pipe and hang plate on J hooks) It won't roll the smoke back into the flames or change combustion chamber shape like a baffle plate should, but is better than nothing and doesn't take away from the limited loading space. It not only prevents flame and extreme heat from escaping straight up, it increases ignition of smoke particles at or near the plate. Flame impingement on the plate does cool the flame tips, decreasing burn zone temperature slightly, but the overall effect is positive reducing smoke particles.
Just make sure the square inch opening all around (smoke space) is no less than the square inch area of the 6 inch outlet. (Perimeter X opening height must be no less than 28 1/4 square inches) If you hang it on J bolts, you can adjust height for opening size to adjust for chimney draw. (the better the chimney, insulated liner, interior, and correct size...... being the minimum smoke space of 28 1/4 compared to a larger flue, uninsulated, exterior, or requiring more heat left up decreasing stove efficiency.
The correct chimney and its efficiency becomes more critical the smaller the stove.