We did it reverse too and had the girls in XL dog crates in the shed.
I made sure to set them up in the middle of his workshop... he was quickly motivated to help get the coop done. The house came with a dog kennel though, so I had an instant run for day time use and we only needed the dog crates for night time. Wasn't my first time with chickens though, I think I'm on my... 5th flock now, over the span of 14 years. First time with ducks though, they're a riot.
You should be able to find 4 hens from the same seller easy enough. At least 8 week old, they won't need heat. About 24 weeks is when they're start laying, so the closer to that they are, the sooner you'll get eggs.
Also, it's super easy for someone new to get taken on gender. Buy old enough birds that it is 100% obvious who is a female. Study photos over in the "What breed or gender" section to familiarize yourself with gender characteristics for the different breeds. Took me a couple of years when I first started out to get to where I can spot a boy or girl as early as day one, depending on breed. Silkies I'm hopeless on, but I never raised them myself. But now, I'm not afraid to buy babies since I can pick them out myself. I don't have to rely on the seller to tell me what the gender is. More than once I've had sellers grab chicks and hand them to me as female, and I set them back down as male. I only buy straight run with ducks, never ever straight run chickens.
I'll buy from swap meats and flea markets, after looking over everything in the booth and thoroughly checking over the birds I want. But I'll likely never buy at an auction. Not the farm auctions I've been to anyways.