I don't have a restaurant but I do have a pretty big, five foot oven. As in any restaurant, the ovens are not shut off during a slow period. The wood ovens, too, rage on into the night. You'll need to figure out what size you'll need and then investigate the several types and brands. Efficiency is key. Wood is cheaper than gas. However, you can't turn a valve and have perfectly seasoned, split wood pour into your oven. It's a lot to consider.
I don't know where you are but can't imagine who would allow a coal burner to operate.
You'll need to make sure you'll have a big enough niche market to support a wood or coal oven. Most people are used to the heavy, cheese laden, cheap pizzas. It's a tough row to hoe trying to get them to like, let alone BUY your pizza. Dude, I make a respectable Neapolitan as good as the wood burning place in town. I'm giving it away and still hear...when are you gonna make the other kind or the Chicago kind?
People cling to the familiar.
Good Luck, It's going to be a lot of work. I'm envious.