"According to the novel Enterprise: The First Adventure, Kirk commanded the USS Lydia Sutherland ... prior to commanding the Enteprise. Although I think Kirk was actually the first officer, and it was his heroic actions here once the captain was incapacitated that led to him being promoted to captain and given the USS Enterprise."
HMS or USS? Just to get this straight: the author was unable to come up with a better name for a Star Trek ship other than merging the names of the HMS Lydia and the HMS Sutherland from the film "Captain Horatio Hornblower" and the novel series?
Sorry, sounds like felgercarb to me.
"According to DC Comics' old continuity, Kirk commanded the Baton Rouge-class USS Saladin for 3 or five years prior to the Enterprise."
Unfortunately I don't have all the comics (wasn't it Marvel?) but think those to nicely fill in gaps unless contradicted by screen evidence.
According to Kirk in "Court-Martial" and the subsequent wishes of the producers USS Republic (NCC-1371) was a member of the "starship class". According to the comics USS Republic was a Baton Rouge Class vessel (of the starship class).
Since USS Saladin was a starship, too, it looks like we have to conclude that Kirk's first command was another ship ("destroyer class") prior to USS Saladin.