Congratulations!

For paint, if you are going to take all of the wood pieces apart and remove the the squares and holes that will hold screws and wood to wood joints, I would recommend using a thin lacquer and give it about 4 thin coats. If you go with a high build paint, the pieces may not fit well and you will end up having to really press thing together which might risk breaking them. Even with the lacquer, I had this problem in two spots. I had to resist the temptation to use the screws to pull everything together because they would star tot deform the nut captive in the wood. My trusty rubber mallet worked, at my kid's suggestion (hurray for brute force).

I went with $5 black spray lacquer from a large retail home improvement store (two cans). I believe Clough42 did something similar.