I have all wire open topped nests, as well as metal 1/2 top nests. I always line the bottoms and sides of the wire ones with cardboard, but I also have a 4' x 8' sheet of plastic that is used to make lens covers for fluorescent light fixture boxes that I have been cutting to size to fit instead. The rabbits tend to shred the cardboard, and the plastic is a reusable liner. I have not drilled holes in the plastic liners, since I have never had a doe soil the nest. (Knock on wood!)
If you use the 1/4" hardware cloth you probably wouldn't need the cardboard because the bedding wouldn't fall out. The whole idea behind having a wire bottom is for drainage, and lining them with cardboard or plastic foils that feature.
If you decide to go with a solid bottom, I would cut plastic to fit because it is not porous like wood, and can be sanitized. Another option is to use polyurethane to seal the wood. Some people use sealed pegboard which has drainage holes.
I use pine shavings and brown paper grocery bags that I put through our shredder as nesting material, plus I put a handful of pelleted pine at the end where the nest is usually made. The does get to add their own hay or straw.
One feature that I really like that the wire nests have is that the front is hinged and held closed with a spring. When the kits begin leaving the nest, the front can be opened so they can easily go in and out. I would recommend hinging one end of your box. As for a 1/2 top, I did have one doe that seemed to think she was nursing her kits when she sat on top of her metal box. The kits were thin until I switched them to an open topped wire nest.