When the Federation Council authorized the original U.S.S. Hood on SD 0965, it was assigned resources under Naval Construction Contract 1707. At the same time, NCC-1703 was assigned to U.S.S. Lexington. Lexington was due to receive an additional command and control package as well as additional defensive phaser batteries. Indeed, 1703 may have been built entirely with phasers, rather than warp-targeted lasers, from the start. Essentially, it would have been an intermediate step between the older YCC type command cruisers and the GCA type cruiser (the actual GCA never had a command variant) in terms of capabilities. 

As we touched on in the history of Yamato, the Class 1 program was at this time largely controlled by UESPA, United Earth's space agency, and there was a degree of political shuffling for prestige in terms of "ownership" over ship names by the various regional commands within UESPA. The Royal Navy, despite its small geographic constituency, had many connections within the United Earth government as well as a long and storied history to draw upon. After extensive lobbying, the Royal Navy faction in UESPA wrangled a renaming of 1703 to acquire the distinction of fielding the first Class 1 command cruiser as U.S.S. Hood. 

We don't have an explicit, canonical answer about the identity of 1707. We do know that the ship existed, because it appears on-screen in Star Trek IV but its name isn't visible, just its hull number.

My best guess on the history of 1707 is as follows:

The Federation Council authorized Hood as a Consititution class ship (improved YCA). At some point no later than 2247, the ship was first renamed Lexington, and then Ranger, which she commissioned as in 2247. She was a YCA at this point. Some time between 2247 and 2271, probably about 2266 or so, she was refitted as a CFS, which was a variant configuration of the Achernar subclass. She never received NCC-2500, that was just an error by historians. In 2271, she was refitted again, probably to the CFS+ configuration (a variant of the Enterprise/Connie II/Endeavor CA+).

We don't know much about Ranger's early adventures, but with her more tactically-oriented CFS configuration she was probably assigned to Military Operations Command and likely played a role deterring Klingon aggression. It's likely she was one of the ships that the Organians prevented from firing on the Klingons in Errand of Mercy. Years later in 2285, during the Ryklah Dagh incident, Ranger defeated and captured I.K.S. L'ktja. That same year, Ranger was destroyed by the I.K.S. Qrish. These final conflicts occured at a time when a substantial amount of Federation fleet strength was deployed on the Romulan border as part of Operation REMUS, so Ranger was likely in the unenviable position of trying to secure the frontier against superior Klingon numbers. 

At approximately the same time, NCC-1562 had nearing completion. She was a light cruiser similar to the Sombra class in configuration - that is to say, sharing most of her parts in common with the Enterprise/Connie II/Endeavor subclasses but with narrower capabilities and less resource footprint. Indeed, its possible she belonged to the Tikopai subclass; while most of the Tikopai type ships were built with exploration in mind, a subset were fitted out for tactical purposes. 1562 (her original name is unknown) was specifically fitted out as a shuttlecarrier escort (NAC configuration) and would have been representative of the light cruisers assigned to ships we've previously discussed like Bong and Fonck. With the loss of Ranger under conspicuous circumstances, 1562 received the Ranger name and was given the 1707 hull number for commemorative purposes (and perhaps to get under the Klingons' skin).

It's unclear if Ranger was commissioned by 2286 when we see her in Star Trek IV. She might have still been fitting out or undergoing space trials, or she might have already been commissioned by then. We can ignore the reference to Intrepid. It was from a deleted scene, and even if we admit it we don't know for sure it referred to 1707. While we don't have details on the new Ranger's adventures, its almost certain that she operated as part of a shuttle carrier or runabout tender task force, since NACs were in high demand as the largest dedicated carrier escorts in use by Starfleet.

We know that Ranger refitted with advanced technology some time around 2292. With tensions starting to wane throughout the quadrant and in particular with the Klingons devoting more and more of their limited resources to contesting efforts by the Interstellar Concordium to enforce the demilitarization of the Klingon neutral zone, the Federation may have seen less of a need for operating carrier task forces and decided to refit Ranger into a less specialized configuration. The most logical refit would be to the NAX heavy cruiser configuration. The Tikopai class, despite its Sombra-like characteristics, was always listed as a heavy cruiser on paper, and its not unreasonable to expect that she had the capacity to grow into a ship of this type.

The NAX type ships weren't used in Operation UNITY because they had less endurance than the full-sized CX types, so after this we can assume Ranger remained posted within the Federation's borders, either dealing with the myriad security threats presented by the Andromedan crisis or simply conducting deep space exploration in areas poorly suited for less capable ships. In either event, her career finally wound to a close around 2314, when she met the fate of the rest of the Tikopai class and went to the scrapper. 

The ship that Victory, like many Achernar acquisitions, started with a different name. She was authorized on stardate 5930 as U.S.S. Za'faran. However, by the time she launched in the early 2260s (several years before 2266), she was commissioned as U.S.S. Victory. Despite her relatively high contract number, Victory was one of the earlier Achernars to enter service, probably only slightly after Achernar herself. We don't know much about her adventures, but she was officially written off as lost, whereabouts unknown, around 2278. 

U.S.S. Victory II was commissioned approximately a year later. FASA indicates that this ship was a Constitution II type heavy cruiser and that it reused NCC-1760. However, other sources list this ship as NCC-1535 and that it was a light cruiser configured as a personnel transport. The graphic novel Spock: Reflections portrays Victory as a member of the Miranda superclass, similar to U.S.S. Reliant. Further complicating things, NCC-1535 also maps to U.S.S. Groton, which was already in service in 2278. Most likely the association with 1535 is an error and 1535 was always Groton. However, it's quite believable that Victory II was built on a Miranda hull. 

If we ignore the anomalous NCC from Star Trek: Starfleet Command, we can probably otherwise conclude that Victory II was a NCT+, which was a light cruiser configuration with improved transport capabilities but fewer heavy weapons than similar designs. It had the ability to transport a very large number of passengers as well as ground vehicles or other heavy equipment and had hangars for heavy transport shuttles that most ships cannot accommodate. During peacetime, ships like this would serve for colonization, evacuation, and heavy equipment transport to remote locations; in wartime, they would serve as planetary landing ships or as commando ships for capturing enemy ships or starbases. 

Some time around 2293, Victory II received an advanced technology refit. It's not clear exactly what class she refitted into as the contemporaneous sources are somewhat unclear on advanced-technology versions of the Miranda family. Likewise, we don't have any data on "commando" versions of the currently-documented "X-tech" ships. Most likely, Victory II's 2290s configuration was something like the DDX configuration, just with the same modifications that distinguish an NCT from a standard NCL. 

In 2294, Victory II transported Spock to a rendezvous with the Enterprise-B for a memorial service for Captain Kirk, who at the time was believed to have died the year before in an incident involving the Nexus anomaly. We don't hear any more about Victory II until about 2315, when she was scrapped. At some point in or before the 2360s, Victory was replaced with a Constellation class heavy cruiser of the same name, NCC-9754.