For your coop AND the conditions that you mention, I'd recommend a dozen chicks. They'd be fine.
While they are growing, you might turn your hand to building an extra coop, or get the local handyman to make some for you. Most commercial coops are made to eventually send the customer back to give the company further profits. I can already see the timbers of your coop as they weather and disintegrate. It will take a few years, but NOT a few decades. An extra coop built from scraps of hardwood would last decades, and you many find it very helpful to have a place to separate some of the birds, or to raise your own. Somewhere for the Hen and her chicks if one day that's what you want.
The coop is great, that one should be a few years, but a longer lasting one will have the roof project beyond the coop for at least 2 or 3 feet, to stop rain, snow, frost, and dew getting on the wood and wire. Something to think of in the coming months. 12 chicks will take a while to grow, 6 months till their first eggs, but it will be worth it. Don't forget to either feed them by hand rather than a bowl sometimes, or give them treats by hand so that they are never afraid of you. Also, when you feed them, practice a call for food so that you can call them later on.