I had this same style of furnace in my old shop.
I built a frame for it so sit on from angle iron, holds it 18" above the floor so the downdraft has somewhere to blow to, and by boxing it in I can direct heat where I want it.
The exhaust stack is simply 3" or 4" flue from the hardware store. Make sure you use double or triple wall going thru the wall/ceiling (there are collars for this at the hardware store as well) I simply used the one from the mobile home, it was well built and triple air-gapped. I ran it thru the wall and with a 90* went on up to a stack making sure to get it to the same heigth or higher than the roof peak. Made a brace for the stack from 1/8" strap metal to keep the stack in place and resist wind movement.
So my exhaust has 1 90* bend right on top of the furnace, 2' of single wall going to the collar in the wall, and 1' of double wall outside. Then a second 90* double wall and the rest is about 10' of double wall with a rain/bird cap.
Worked excellent.
I only ran it when I was out there working, so 100 gallons lasts me roughly the whole winter. That's running it in the evenings a few nights a week for a few hours, and occasionally the whole day on a saturday or sunday. My 2 car shop is well insulated both walls and ceiling with reclaimed fiberglass batts, but my doors are old wooden things with no seals.
<<<< You'll notice my new shop is slightly different. I need to build walls and ceiling to even begin to think about heating an old barn!
Good luck!