We have several different Bluebird houses, and the one that they choose most commonly is this Peterson style house.
https://www.dutchcrafters.com/Amish-Poly-Peterson-Blue-Bird-House/p/54509
Tips for building your own Peterson style here. https://feltmagnet.com/crafts/bluebird-house-slant-front
They’ve also built nests in this one every now and again.
https://www.lowes.com/pd/10-875-in-H-Cedar-Wood-Variety-Nesting-Box-Bird-House/1000184213
This one is pretty similar to the third one that they’ve used sometimes.
We also have one on a post that we bought from Wilds Birds Unlimited, but the House Sparrows fight for that one, so the bluebirds never choose it. I keep it regularly cleaned out so the sparrows never lay eggs in it.
I cut standing dead trees for firewood but I don't cut them down if they have any holes that could be used by a critter for housing. That includes woodpecker holes as we have plenty of them around here. Nothing cool has moved into any of them yet though.