Any of those can work.
I think you should build the coop first, then get the chicks.
Chicks always seem to grow faster than people build coops, so building the coop first helps avoid problems.
Research how much space chickens will need when they're grown up, think about how many, and be sure to build the coop big enough.
Some people brood chicks in the house for some number of weeks, but it is often possible to brood the chicks in the coop from the first day. You just put the heat lamp or brooder plate in the coop, check the temperature over a several day period, and then go buy your chicks and put them there. (The temperature checking is to be sure it's right for the chicks, and also to reassure YOU that it's right, so you won't panic the first night.)
It's probably best to keep the chicks in just the coop, not the run, for at least the first week or two. After that you could pick a day with nice weather and open the door to the run so they can explore. It will be big and scary at first, and they may just peek out the door, but pretty soon they will like playing in the run. Just make sure they all get back inside before dark--they sometimes need a bit of help to learn that.
