What is the best trigger for an ar15? If money was no object, what would be the recommendation? What exactly is the difference between a single stage vs. two stage trigger?

Knight's Armament 2 stage trigger is the best made.  I paid $275 for mine but sold an extra I had for $240.  Sorry no more to spare.  You will find them listed from $250-275 and they are somewhat hard to get.  Trigger drops in in less than 5 min with no tools even if you have no experience swaping triggers.  It comes with two springs.  One for a 4.5# pull and another for a 3.5# pull.  I suggest and use the lighter one.

Probably the best options on either end would be the Accuracy Speaks or JP single stage trigger, or the Knights double stage.

Single stage trigger has no creep, no over travel, no pull so to speak. Just apply a specific amount of pressure and the trigger breaks crisply and cleanly.

On a double stage, you have a light first stage of pull, then as you reach the end of the first stage pull, there is a light let off second stage.

JP is a little nicer single stage trigger with more room for lighter adjustment. But it uses set screws to achieve this greater level of adjustment. Some folks do not like the fact that a trigger uses set screws as they may not "set". The Accuracy Speaks trigger is also very nice, but not quiete as light as the JP. However, because of it does not use set screws, it is inhernatly a tougher, more robust trigger group.

There are many types of double stage triggers. I have never used the Knights, but everyone I know or have read about whose used one says there is nothing else like it. The Knights trigger is not as easy to come by commercially, and is quite expensive.