The biggest pitfall in finishing drywalling (for the DIYer) is sanding in between coats. This will quickly introduce waves into your surface which will cause you to sand even more. The end result will be a big mess and a poor finishing job. Instead, don't sand after each coat, but use your taping knife to knock down the surface flat. Your surface does not have to be perfect for the next coat, just flat. So if you have a drag mark, it will be coated in the next coat. Bumps or ridges, however, must be knocked off before the next coat or the next coat will not go on level. I only sand after all the coats are on, and then only lightly. For more tips on finishing drywall go to
Drywall Finishing and Taping Joints For The Beginner - How to Drywall .
With respect to your ceiling, if you are concerned about the strength of the furring strips, then simply get some longer screws that will go through furring strip and into the studs to help with the support. Make sure to mark/measure your studs off before putting the drywall up so you can easily find them. You will want either a drywall lift (you can rent one) or one or two T's made from a 2x4 with a flat board to hold up the drywall while you fasten. If you are doing this without a lift, you will want a friend or two preferably to help. Use 5/8 inch drywall for ceilings - it is code in many areas.