What was the first Federation flagship/starship in service?

Question

Did the Feds have any classes of or starships in service before the NCC1701 Enterprise? I'm curious as to the history of the space exploration operation and which ships began the first voyages into the final frontier.

Answer 1

In the excellent Star Fleet Technical Manual, the Federation Charter states that the 'Star Fleet' will initially consist of planetary fleets and that members also agree to fund the design of a fleet specifically for Federation use.

Article 43

All members of The United Federation, in obligation to the maintenance of interplanetary peace and security, agree to make available to Star Fleet, on call of the Federation Council, armed forces, assistance, and facilities, including rights of passage, necessary for the maintenance of interplanetary peace and security;

Article 52.

1. There is established a Star Fleet as the armed peace-keeping forces of the United Federation of Planets. It shall initially by comprised of contingents assigned to it by members of the United Federation of Planets under Article 43 until such time as facilities, recruitment, and training obviates the necessity of drawing upon the armament of any member

Article 53

1. Initial expenditure is granted under these articles of Federation for the design, procurement, and operation of fourteen (14) heavy cruiser type of starships to provide the nucleus of Star Fleet's peace-keeping armed forces. These cruisers shall be capable of extended duration patrol of intra-galactic range, with weaponry appropriate to such class starships. They shall be provided with fire-power superior to that now employed by any member of the United Federation, and appropriate to the tasks expected of them;

Therefore the first classes of Starships weren't specific classes but rather fleets provided by members. The very first 'class' of ship designed specifically for Star Fleet was a "Heavy Cruiser Type of Starship"

Answer 2

Well, Yes. The series Enterprise explored the voyages of the NX-01 "Enterprise" which was the first ship of Starfleet, before the creation of the Federation.