I've done a handful of these. Maybe it's not a popular idea, but I like to shoot for museum quality results. Some would prefer the patina, but to me it's a case by case call. I would recommend coating the brass with a lacquer or something, otherwise that nice shine you worked so hard to get will be dull in no time. Fun stuff though and a fun watch!
I enjoyed the video, nice to see old thing smartened up. If you want to have it working properly - assuming it is in working condition - you can use the adjusting screw on the back to centre the black pointer to " 12 o'clock" ( not quite correct but close enough ) and then turn the brass knob on the front so the other pointer covers it. Leave it for a day, maybe give the knob a little tap to wake up the spring below it, and if you see the black pointer heading counter clockwise, that means there's rain coming, how far it goes will indicate how much is coming, and it's clearing up to finer weather if it goes the other way. Barometers are way cooler than smart phones.