If you have never hired drywall installers before, the biggest issue that I run into with them over and over again is clean up. If they are allowed, they will make a mess like you cannot imagine!!!! Be sure to know how much material you are buying, and how much they use before paying them. It's not uncommon for a lot more sheets to be delivered then are needed, and they charge you for all that was delivered, and then they keep all of the extra. I've seen 30 to 50 sheets extra on a job!!! Be sure to insist that 5/8's drywall is used on the ceiling. NEVER use half inch unless the ceiling joists are 16 inches on center. Half inch will sag over time on anything farther apart then 16 inches. Be sure to have in writing what you want the floors to look like when they are done. If you do not say anything, there will be joint compound and scraps of sheetrock everywhere!!!!!!
NEVER make your final payment until you are 100% happy that they have done everything the way you want it. Once they get paid, they will be too busy to fix anything. If they have not been paid, they will find the time to get it done, and this includes clean up and hauling off the extra sheetrock that you do not want to pay for.