It all depends on who you want to believe. According to Paramount Studios, the NCC-1701-A is a Constitution-class ship, originally named the Yorktown (this is the the theory favored by Gene Roddenberry). As the story goes, the Yorktown was damaged during the Whalesong Crisis (ST4: The Voyage Home), and was later repaired and renamed in honor of Captain Kirk.

In his book "Mr. Scott's Guide to the Enterprise" (definately not canon, but who cares anyway, it's still Star Trek), however, Shane Johnson states that the ship that was renamed was actually the Ti-Ho, a new-build ship. (This theory, to my knowledge, is not favoured by anyone, with the possible exception of Mr. Johnson himself).

To further confuse things, the book "Ships of the Star Fleet, Volume One" (still not canon) by Todd Gunther states that the new-build ship that was renamed was actually the Levant (This theory seems to be the one favoured by many treknologists).

According to Roddenberry and Johnson, the NCC-1701-A was a Constitution-class ship. Gunther states that she was Enterprise(II)-class, as the 8 Constitution- and Constitution/Bonhomme Richard-class vessels upgraded from 2268 onwards (including U.S.S Enterprise NCC-1701) were called the Enterprise-class.

The following specs were shamelessly copied from "Ships of the Star Fleet, Volume One" by Todd Gunther.

211,500 metric tons standard.
Two LN-64B Mod 3 dilithium-energized antimatter linear warp drive units, Two RSM subatomic unified energy impulse units, QASR particle beam maneuvering thrusters.
Warp 9 standard, Warp 13 Maximum.
5 Earth years standard, 25 Earth years maximum.
510 (74 officers + 435 crew).
6 banks of 2 each - RIM-15A independent twin mount, 6 banks - RSM-20B single mount.
Photon Torpedoes:
2 tubes - Mk 70 Mod 2 direct.