Example of the differance that having an effective maritime force could make - from ancient times.
The Battle of Thermopylae is the famous battle of the 300, however the object of this stand was not to defeat the Persian Army, but to buy enough time for the Greek Navy to inflict enough damage on the Persian Navy that it would not be able to resupply its land based army.
In the event, the sea battle was a stalemate, but enough damage was caused to the Persian Fleet to slow them down, ultimately enough time was gained for the Greeks to regroup and inflict a heavy defeat on the Persians at the Battle of Salamis.
Its this defeat that ensured that Persian land based army could not be resupplied, and its this that lost Persia the war, you’ll note that land based resupply was not reaslistic, not enough material could be moved quickly enough to keep a sizeable army moving.
Even a fairly modest vessel would be capable of shifting a hundred tons and more -and only need a dozen sailors to do it - to make long journeys over land to shift a few thousand tons of supplies - probably using asses and oxen you are looking at far more time, far more men, and you would use up a goodly portion of your cargo just keeping the carriers going.
Moving cargo by sea might have a high initial cost before you start moving anything at all, but once in place, it would then cost very much less to move large amounts of stuff about, it would be faster - much faster, and would be safer.
If you had a military leader, they would commandeer suitable vessels or be required to return some sort of military service in return for trading rights and protection, so the cost to the rulers would probably not be all that great.
If you are going to put shipping into a wargame, then the main issue would be the length of time of the conflict, balanced against the rate of lossess incurred by the fleet - it would probably not be possible to replace a signifcant loss in a short period of time, it would certainly take months to replace shipping and possible a few years.
War campaigning was in distinct seasons where conditions would be more favourable, heat, storms etc and also suitble winds to shift good about on your boats.
You could have a build up of maritime forces, and of cargo vessels, it was quite normal to move your armies around by sea, but then you could set a scenario whereby loss of shipping cannot be readily replaced, and thats when seizure of enemy vessels and repair of damaged ones becomes absolutely crucial - and this means having materials avaliable to do those repairs, nearby shipyard facilities etc.