First question is how much are you willing to spend if you're hiring someone to do this work?
30' feet to the house isn't bad. I'd strongly recommend running one or two 120 volt, 20 amp circuits from the house, buried at least 18 inches underground. You'll probably only need one of those circuits but it's always good to have a spare for the future. And once you've paid for a ditch to be dug and conduit to be installed, the cost of an extra circuit isn't significant. This assumes you have a spare space or two in your breaker panel to use.
I mentioned conduit. Don't run direct burial cable. Protect the wiring in PVC conduit. It's not very expensive once you've gone to the trouble of digging a trench. I've seen a lot more problems with failed circuitry over the years due to direct buriel wiring than with wiring installed inside conduit. Pull (5) 12 gauge single copper conductors (solid or stranded, doesn't matter) through 3/4" PVC and you'll be good. That will give you two hots, two neutrals and a ground. You don't need 10 gauge if your coop is 30 to 50 feet from the house. (Assuming the total run isn't an additional 50-75 feet to the panel once you enter the house.)
You don't need a breaker panel in the coop for one or two circuits. Terminating the conduit into a 6" x 6" PVC junction box will suffice. From there, you can branch out to switches, receptacles and light fixtures.
I wouldn't bother with an air conditioner. As one previous poster mentioned, you'll have more problems than it's worth. Just give the chickens good ventilation and they'll be okay.
Again, what are you willing to spend? If you're willing to do the digging yourself, or rent a trenching machine, the electrical work beyond that shouldn't cost more than $200 to $300, aside from whatever light fixtures you select. I've been doing this stuff for 25 years and that's a realistic number. A licensed electrician may or may not be required, based on local ordinances... but I'd make sure whoever you hire is insured and comes with favorable references.
Whatever you do, make sure you do it right the first time. It always costs more to do it twice, due to lack of planning and due diligence.