I have always wondered this.
In Ent it seems there is 1 and later 2 long range ships and a dozen or so short range vessels like the intrepid. As far as registration numbers go we see NX-01 and 02. Yet there are otherships that were built before hand like as I said the intrepid (what would their reg number be?)
TOS we know there are at least 12 Constitution class vessels. With this number going up by the time of Undiscovered country. And there are a number of other classes in the background either on displays or shown like the Grissom or Excelsior. Also the highest reg number we see on screen is NX/NCC-2000. so there is at maximum around 2000.
By TNG/DS9 we know there are thousands of ships due to the whole dominion war. We also see a multitude of classes on screen. We also have the higher registry number as NX-74913 on the Prometheus. So there is a maximum of around 75000 ships.
Few things. Just because we don't see other classed in TOS until the films does not mean they don't exist as the reason they were not shown is most likely budget restraints.
As for registry numbers it can be assumed they cant give a completely accurate picture as older ships with lower registry numbers would be decommissioned. Though to confuse matters registry numbers can be reused as we see the Enterprise always carrying 1701.
Also seeing as the lowest Excelsior class is NCC-2000 and the highest number is USS Melbourne NCC-62043 it seems there was a massive fleet build up around the mid/late motion picture era. (maybe due to possible Klingon war? Federation expansion?)
IM also assuming the Excelsior and Miranda most likely were discontinued to be built by 2340 as the design of the ships change as we can see by the ambassador class. why built old designs when new ones come out? You would just then refit the old ships rather than build new ones.
In conclusion my theory is.
Around the TOS/ Early part or the motion picture era the fleet size is most likely around 1000/1500.
By around the undiscovered country its gone up to around 20000-40000 ships.
By TNG the fleet size most likely decreased by a unknown number due the relative peace with only really the cardassians to worry about. So allot of the fleet would be in mothball.
By DS9 the fleet would be back up to the 20000/40000 level due to the Borg and Dominion.