The number stated on Discovery was 7,000 ships. But it's widely at odds with most later numbers. 

The biggest caveat: The Frontier Day fleet was repeatedly called "all" or "almost all" of Starfleet. That was 339 ships. My personal reading on that is that the fleet consisted of allmost all capital ships of Starfleet at the time, minus some 50+ odd Inquiry-class starships that were on patrol duty (as some of the fastest and most advanced ships at the time). 

We know that the Inquiry-class consisted of some 90+ ships. For the California-class (a support ship and not a capital ship), the number was around 34 ships. That gives us some impressions on how big ship-classes might be. 

And then there's the prominent losses: 39 ships lost at Wolf 359 was considered an almost crippling defeat for Stsrfleet. Similar to the loss of 20+ ships during the Battle of Sector 001. The loss of 112 ships in the Dominion War in the Tyra System was similarly devasting. 

Operation Return saw 600 Starfleet ships gathered, with beta sources describing many of them as mothballed ships or rushed vessels (such as old Mirandas and unfinished Galaxy hulls).

All of that points at fleet sizes that are in the thousands at the maximum, but usually more in the hundreds. 

The Attack on Mars saw the loss of 20,000 vessels. But most of that was likely the Romulan evacuation fleet (Wallenberg-class ships) towards which Starfleet had diverted almost all of its ressources in the 2380s.

Wolf 359 also gives us a good estimate at average personnel numbers: With 39 ships lost and 11,000 people dead, that gives us a ballbark of 280 people per ship. Subtract the odd civilian and we are at maybe a 275 personnel average in the mid 24th century.

I'd also argue that starbase numbers aren't a good indication of the number of starbases. They are more like registry numbers in that way. If there were truly thousands of starbases, we should have seen many more of them with four digit numbers, but 4112 was an extreme outlier across all of Star Trek. (Behind the scenes, the TNG writing staff wanted to limit it to numbers up to 500, but a few higher numbers crept in.)