1/350 would seem to be the logical choice for sheer availablity - with more and better-detailed projects to choose from all the time - but the smaller ships are likely to come in a bit under your 18" window. Larger scales are available, with newer 1/200 stuff coming out, and a somewhat random spread of older ‘box scale’ kits still readily acessible (like the old Revell 1/240 four-stackers). It just depends on whether you want to stick with one consistent scale - which it seems is your object - and how much display space you’ll ultimately have available. [:D]
To keep around the 18" desire you may want to look into the Revell 1/144 Flower class Corvette which ends up being 17+“. Any destroyer or escort in 1/350 will be around 12” or less.
As far as subs, a 1/144 Gato will be around 24 inches, U-boats will be around 18 inches.
As far as not enough parts, plenty of PE out there to dress them up and get a better scale effect. That will add to the parts count and hair pulling, not to mention the language skills. Available for pretty much all the US, German and Japanese subs in that scale.
Gato’s in 1/350 (AFV) are about 11-12 inches, but PE out there for them as well
With respect to small navy ship models in general, although I have a copy of the Lindgerg 1/125 scale Minesweeper, I’d love to find a similarly large scale model of a newer mine counter measures ship like the USS MCM-1 or MHC classes, the RN Hunt class or the European Tripartite classes. [:)]