Again your comments sound right however I would add a few nore points to what has already been mentioned. pre-2270 Constitution Class -main work horse of the fleet
However as SOL has already mentioned the roles it used to perform were being taken by other ships after 2270. There is also the constellation class and that was designed as a deep space and long range exploration vessel. The stargazer was assigned a 22 year deep space mission (seemed quite a long time). It was more heavily armed and basically a better replacement for the constitution class.
By the start of the century the ships therefore were Excelsior Class ships which were the workhorse, miranda and her variants for patrol, science and transport and finally constellation for deep space exploration. The Oberth Class would also remain in use due to excellent performances as a science vessel.
Although by 2370 there is the constitution class variant and the intrepid-constitution class variant in service (if you believe in the designs in the DS9 tech manual).
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