Installing Drywall on Concrete Ceiling?
In apartments that I have renovated it is standard to install metal channel furring strips.  If you want depth you cross these with 1x or 2x4.  The channels you glue and screw into ceiling.  The wood is screwed into the channels.  There are plenty of LED lighting kits that are sold now that can fit into 2-3 inches of space (remember you have the drywall thickness too).

Just to add some clarity we use channels that look an awful lot like 



The difference is ours has preset holes on the lips for drilling, the lips are a little wider and I am pretty sure it is a thicker gauge than this.  Do not use the cheap/thin metal furring strips from big box.  They might work for concrete walls but not ceilings.

Also to give more detail:


We install these every 12-16".  12 if doing 2x lumber which I think we have done once.  The installation is dependent on the type of concrete.  Often the owners of the property have told us what other have used and we follow that.  Most of the time it is tapcon with semi-predrilled holes.  Note that the strips should be glued before being drilled.  Also note that the stronger the glue the more chance you take out chunks when uninstalling - that's a different question though.  For the screws practice before you go in with a plan.  Don't buy 300 of a type of screw and then find it will take 20 mins per screw doing it that way.  How many screws you need is dependent on the flatness/shape of concrete and how well the furring strips have contact.  Most installs I have done were two screws on the ends and then stagger sides every 12-16".  A 20' strip might have just 15ish screws.  
We leave a small gap (1/8th") on each wall and try to run them the entire length.
We then install L channels on the two walls that hold the ends.  We try to get a very thick gauge and hammer L channel up so that it is effectively holding the channels.