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What I mean by this question is that the ship should follow the basic anatomy of the protagonist Enterprises such as the Constitution and Galaxy classes. I.e. they should have two nacelles connected by distinct pylons, primary and secondary hulls, some sort of saucer section, etc.
Is there something smaller than a full-blown starship such as something the size of the USS Defiant or a shuttlecraft that follows this plan? Or are the NX-class and the Freedom-class the limit?
"two nacelles connected by distinct pylons, primary and secondary hulls, some sort of saucer section"
It's crew module is more of a tea-cup than a saucer, but with two nacelles on pylons, a secondary hull made from a surplus nuclear missile and a primary hull made of scavenged titanium, Cochrane's 'The Phoenix' seems to have been the first and smallest of that formula.
https://memory-alpha.fandom.com/wiki/Phoenix?file=Phoenix_top_view.jpg shows clearly the crew module is attached above the narrowing of the missile's nose cone rather than being a single part of that hull.
It turns out there's not an easy way to answer this, because canon is sloppy or missing.
The Oberth class meets all the requirements at 120M (per Star Trek III production notes). But, as the link above notes, it's got massive logistical problems with that number
If the Oberth were only 120m long, there would be only two complete decks of only 2m clear height inside a saucer of 39m diameter for the lower deck and 32m for the upper deck, respectively. The small saucer would have to include the standard-sized bridge, a computer core, quarters for 80 crew members, three cargo bays and, of course, several science labs as we expect it on a dedicated science ship. The window arrangement with the useless "skylights" for the lower deck, at the expense of some area in the upper deck, seems idiotic, unless it's something else. No need to mention that the Lilliputian decks of the 120m ship would not match what we have seen as interior sets in "Star Trek III" and four TNG episodes.
As such, the Oberth class is probably closer to 150M at its smallest, and possibly more than 200M by the time TNG rolled around.
The Daedalus class seems like a better candidate. They were 105M or 140M long and meet all the requirements of having distinct nacelles with pylons and a split hull design (with a giant ball instead of a saucer, but close enough). The catch is we have no official canon specs, so subsequent mentions vary, but some official-ish sources peg it in at 140M which seems workable
[Maybe the model's windows are wrong] in order to allow the ship to be composed of 15 decks of 2.8m each, giving us an overall length of 140m. This is just a compromise, but it keeps the ship reasonably small compared to the Constitution class, while it alleviates all the problems of the 105m Daedalus. The size comparison with the NX class and the Constitution class demonstrates that the Daedalus class works well at a length of 140m.
If we're limiting ourselves to pure canon, this is probably the only acceptable winner. At around 225M, this is the smallest we can be certain meets all the qualifications. With ST: ENT revolving around a single ship, we know how this class was laid out and how big she was. There's no TOS or TNG era ships that were this small and it's hard to find many below 300M, let alone far below.
"Classic design" I assume you mean TOS? or the saucer/body/nacelle design.
The smallest is the "Nova class" the ship comes in at 221 meters in length and follows the classic design philosophy.
"Size according to main website"
https://www.startrek.com/article/inside-the-u-s-s-equinox-ncc-72381
Never the less, approximate size is difficult to determine without placing against Voyager.
The ships Master system display extrapolated against pixels, show it to be 198 meters in length.
