Mess is fine by me. I'm already extremely obsessive about cleaning, since I foolishly have a macaw and a grey in the same house. Air purifiers run 24/7 and everything is wiped down at least thrice a day. I'm just unwilling to further endanger my New World fids with more dusty birds, so I'm glad my budgie trio won't add to the dust to a noticeable degree. That's a relief!Budgies don't produce dust like cockatiels do, but they are quite messy for their size just to warn you. So they might still produce respiratory symptoms with out frequent cleaning up after or ventilation, especially in warmer conditions.
Edit: By the way, I am really glad there are people like you who are willing and able to take in unwanted birds. You have a big heart, and I wish you the best. Just remember not to bite off more than you can chew and to take care of yourself first and foremost.