Ditto Dat^^^Do your homework before you buy 6 month olds too. it would be really easy for someone not honest to screw you over with sick or old hens, or a rooster that no one wants. maybe you'll just want to wait til next year then you have time to make sure the coop and run are good, settle in, and do more research with breeds and care, then start with chicks next year. Raising chicks certainly hasnt been hard.
Good luck with your new home
Chickens can be very easy to care for.... after you climb the learning curve, and it can be steep!
There are a lot of little things that can make maintenance and daily care much simpler, and there are little things that can be a PITA to fix after the fact.
There's a lot to learn about housing, feeding, predators, behaviors.
Housing is the biggest issue and it sounds like you might be ahead of the game there depending on what kind of coop comes with your new place.
I fully agree that moving to a new place and starting out with chickens are both time and resource demanding, but then I don't like dealing with drama, emergencies actions and animal crisis', I'd rather wait and plan to avoid those things.
Another aspect of getting older chickens vs chicks, is bringing in disease and pests with older birds. Planning to house chicks ahead of time will serve you well in the future, because there will always be more chicks down the road and having the facilities to deal with them is nice.