Reading through this I could some help,congrats on your stove.
So you already got the fire starting thing situated, on an established fire *all pieces are burning, flames in the fire box are vigorous in nature you want to cut your air supply in increments. If you take your adjustment rod and 1/4 it up, that will work best, the idea is that you want semi lazy flames in the fire box, and you want to see secondary flames coming out of the air tubes, everyone has a slightly different setup with different draft parameters so my fully closed air rod may give you the same effect at a 1/4 open.
The thermometer that you have, you need to confirm that its a stove top one and not a single wall chimney pipe one, chances are you have a chimney pipe thermometer (most prevalent) and if your running it on the stove your probably running the stove on the cooler side of the safe burn level. Once you have the proper thermometer your shooting to have the stove cruise between 550 and 650 deg, until then use the chimney as your guide, if your burning seasoned *dry wood <20% moisture content then you shouldn't be seeing any smoke coming out the chimney, only heat vapors. Your front glass should remain fairly clean, although a thin haze may develop, you should not have any thick black deposits on the glass, especially in the middle region, sometimes the corner get a little dirty, but that's not a big worry.
The idea with reburn stoves is that once the stove is rolling along, the air should be turned way down, again lazy flames with a gas like furnace flame coming out the top tubes, this is where you get the stove efficiency, the smoke is reburnt, the firewood isn't burning crazy fast and you have optimal heat transfer, keeping the air more open sends more heat up the chimney, but you have to find your happy medium, *fiddler alert
! after making each adjustment, let the stove settle down, this can take 15min after each adjustment, especially when learning how to dial it in.
Tools that you should be interested in, a good pair of welding gloves with longer sleeves for hot reloads, stove top thermometer, or hand held infrared thermometer, a good ash bucket with lid, moisture meter for testing firewood splits, and a metal garden rake to rake coals forward to burn them down. Oh and grab a 12 pack when dialing in / learning your stove.