Are you buying a new chick or a new pullet? If you buy a new chick it will have to be put in it's own brooder away from the older girl. The pullet would not accept the newcomer right away, and being a chick (which is WAY smller than the pullet) would likely get it killed. I suggest either buying a same-size pullet or two from fair (and keep them sepperated for a few weeks so any illnesses can become apperant) and then let them live in the same coop sepperated by wire for a few more weeks before taking it away.
Or you could buy two or three chicks (they don't brood well alone) and start integrating with wire when they are close to the same size as the pullet.
A cheap coop is usually a coop that used to be something else. Doghouses, playhouses, pallets, sheds, furniture... the list is long. Make sure when you build or modify the coop to build a:
) waterproof roof,
) plenty of ventilation (as high on the wall as you can get it, and a copula from Home Depot is great too),
) a nest box for later,
) a roost (2x3's, 2x4's and tree branches are good roosts- keep them a foot off the ground or more),
) and calculate the floorspace- make sure each chicken has at least 4 square feet of space. This does not include space taken up by feeders or waterers, or nestboxes.
