Bearing in mind that the Pheonix made it into the Warp "One Point Somethings" and Archer remembering his father's work with Warp 3 (27c) engines, early Earth starships would be rather on the slow side.
The Fortunate was only capable of Warp 1.8 or around 6c where as the later built Horizon just made it past Warp 2 (8c).
So if, as abenchmark, Starfleet's starships would be probally only one small technology step more advanced than the Fortunate and the Horizon.
So with early Starfleet pre-Ent exploration starships pushing in the Warp 2.5 (15c) to Warp 3 (27c), and interstellar flights to even local stars of interest, most of the ship's hull would be for stores and supplies.
On the other hand, the Warp Nachelles would be smaller than the NX-01 but larger than on the Horizon or Fortunate.
A balance between speed and Warp Streamlining against flight duration (stores and supplies) would have a strong influence on the design brief Starfleet would hand to the engineers and designers tendering for an exploration ship contract.
Remember, compared to the NX-01, early Earth Warp powered starships, would be like sail ships next to a steamer.
Just something to bear in mind.