The military in the duchy of Feann has two main goals. Defend the duchy and its assets as well as making sure the duchy fully protects the external borders of the kingdom. It is hard to say at the moment what the biggest threat will be that the duchy of Feann will face but some examples would be pirates, thieves, enemy kingdoms and internal threats within the kingdom.
Defending against each threat will require different tactics. Protecting trade from pirates will need a navy as will protecting trade from enemy kingdoms. Protecting against thieves will require trade routes to be patrolled by the army and protecting against internal threats will require a well-defended border (both external to the kingdom as well as internal).
As laid out in the transport page the initial priority is protecting the duchy which will mean major roads will take troops from their barracks to the areas that they have been assigned to defend. Of course, food and supplies will also have to use these roads to supply the troops so it will benefit that as well. Furthermore, the navy will defend sea-based trade for the same reasons.
It is too early to say what the funding will be for the military since there is very little that we know of so far but the duchy will always ensure that it is as well defended as possible within the constructs that the game lays down.