I'd ex[ect the ships to be radically more primitive though some of the races have had Warp technology longer than the other, namely the Lyrans, Kzinti and Hydrans. The Klingons only aquired Warp Drive somewhere in what would be Earth's early 20th century. Earth, itself, is the new kid on the block in terms of interstellar travel.
I'm more interested in further back than this, perhaps around the time of the earliest hostilities between the Kzinti and the Lyran. SFB history has them at war with each other for at least 500 years before TOS. They would need Warp Drive technology to achieve this. The Hydrans probally aquired Warp Drive at least 400 years before TOS.
As warships are so limited for power and the weaponry available so feeble, space battles would have involved large armadas so that combined firepower could be brought to bare onto an enemy.
I've uploaded the Kzinti Fusion Warp Drive fleet that I've been working on in Final Products as an example of what I mean by early as in very early.