They sound excellent. The bin you have sounds like the Samla bin which is about 78x50 at the top but narrower at the bottom. Many people think 75 x 45 is a good minimum for a dwarf hamster but their personalities vary and some are happy with something a little bit smaller. How you set it up will make a difference too.
To paint the wood people use plasti-kote water based enamel paint which is safe but they're only little pots so perhaps not great for a large area like a cage - although if it's just for the inside then maybe 4 pots would do it. I'll link them.
Rodipet sell a bigger tin of something similar - water based - called Auro I think.
https://www.amazon.co.uk/gp/product/...?ie=UTF8&psc=1
https://www.rodipet.co.uk/houses/aur...sh-0375-l.html
They sell a brush to go with it too! I just use a normal household paint brush.
https://www.rodipet.co.uk/houses/aur...rush-40mm.html
The rodipet tin is bigger.