For ease of construction, I painted all my panels inside first before assembly. Some have masked off the areas that get glued before painting. Be aware of using water based paint on MDF! I've not tried water based paint.
I used yellow wood glue between joints, applied with an acid brush for a thin coat.
After assembly I sealed all joints with an adhesive sealant (as posted in my reply above) and smoothed the sealant with a wet finger. I have discussed this with a few cabinet makers and it's what they suggested for this type of build.
Some have painted the inside after assembly. I'd be afraid of not getting it all covered? But, that's just me
My first build I used drywall screws, I now use cabinet screws. From research they are less prone to breaking during install and use. All holes are pre-drilled and the first panel that the screw goes through was drilled for clearance and countersunk. You can buy a drill that does both in one operation. I purchased a drill depth stop attachment for a couple of $$'s so all my holes would be the same depth that I now use.
I've encountered nobody having any serious issues with a build not working doing how every they have done it. Small leaks here and there which they had to track down after it was finished.
Outside of my cabinet was painted using Rustoleum with a foam roller. I did not thin it out, if I did it again I would thin it some, I had to sand it between coats it had a course texture. But, it came out really really nice, seems to be very durable and it was cheap to do for an excellent finish! I used around 1 quart of paint and put on 3-4 coats?
Some builds have been "wrapped", professionally painted, brush painted, roller painted or not painted outside. All move air which is what they are suppose to do, it's not a classic show car. I understand the attention to detail though some put in to this project!
Keep in mind the
INSIDE needs to be painted or it's going to leak air!!