Well that thing has stood for however many years, so as long as the roof doesn't leak and it hasn't already blown over, I would not be too worried about it. But I live in an old farmhouse where the corner stone is from 1898, so I may feel differently about these things...haha!
I would line the edges around the bottom with the hardwire mesh angled against the floor and walls to prevent anything from getting in. Then I would line the inner walls with plywood up unto a foot and a half or two feet from the roof. Use more mesh from there to the roof, so the top bit gets ventilated through the slats. Built in ventilation!!! Awesome!
On the inside you can use chicken wire to separate, since you will only be keeping chickens apart, not predators out. Make a few side-by-side rectangular runs so you can allow chicks to meet each other before integration. I would also make it so that the runs have pop-doors between them so the chickens could have use of all the space once integrated.
Set it up like this: Walk to the human sized door into an entry way with storage tubs and the doors to the parallel runs in front of you. The runs go back to the back wall, where you can have small pop door sized holes cut into the wood that can IDEALLY be operated by a wire without having to go into the pen. Build a run off of the back of the building.
You can have pull out nesting boxes lined up on the walls, with the openings facing the wall, and a little sill they have to climb over to get in. Build little hinged doors on the backs of them so you can get the eggs out, and if you need to clean them out from the bedding, just slide the whole set up off and dump it on the floor.
Make roosting bars with poop boards underneath - you can make the poop boards into sand trays and use the horse stall refresher sweet PDZ on it - then you can scoop the poop off like cat litter, and it will smell better.
That's how I would do it. Do you have electric or water near there? You can look into making water tanks that use a nipple system, or use adjustable height hanging food and water, and you can keep it by the human sized door.
Have fun with your project!! You have a beautiful family!