I think nuclear weapons would not be used as kill vehicles: the effective radius (small due to no fireball, the damage done would be from flash-heating by radiation) probably does not justify the cost of not simply using more kinetic missiles, but it depends on the technology. However, nuclear weapons could be very useful for point defense or scaring enemy sensors into temporary shutdowns.
It is impossible to be invisible in space, but lowering the detection range enough that the enemy has limited time to react is very useful.
At the speeds ships would need to move at to make space travel plausible, nothing will survive a decent-sized kinetic impact.
All of the following depends on non-instant or no FTL, multiple "baskets" controlled by different powers, and some regard for human life:
Space war would be focused on denying the use of resources, supply centers, and ultimately populations to the enemy in order to force concessions: I would expect expendable, dedicated military drones relying on other traffic to not be immediately spotted, and no armament on other assets to prevent them from being destroyed unnecessarily. The goal would be to place the other side in a position where they would be forced to submit or suffer massive economic and population damage - similar to the theory of war, if not the practice, under mercintilism. Ground combat I would expect to be extremely bloody, but in space anything with strategic value would be as distributed and expendable as possible to make it harder to force them being denied. (meaning that they could be forced to surrender or be destroyed, either one would be a losing proposition). Commerce would be heavily regulated and patrolled, because getting undetected a force into a population or logistical center would be a major bargaining point for any involved power. This assumes that no participating powers are terribly fanatical or completely desperate, because such a situation would probably end in mass genocide for everybody.
I see a few types of military ships:
Defensive or patrol ships, based at areas of importance and keeping the area threatening it as well as any maneuver areas (jump points if they are a thing, anything that could hide ships, etc...) clear and checking any incoming craft. These would be most extensive around civilian centres, as their location cannot be kept secret, which is the first defence of military installations assuming interstellar travel: stealth may be futile, but space is big.
Offensive ships, those designed to get in and deny enemy assets and those supporting them. These could be disguised as commercial shipping, "stealthy" buses carrying KKVs, or any number of other types.
Deterrent weapons: nuclear or massive kinetic threats to civilian populations, enough to scare the enemy into not using theirs on you. "The bomber will get through"; it is impossible given reasonable technology assumptions to defend a planet against unlimited warfare, so these would be the equivalent of the nuclear threat today. These could be asteroids with engines, FTL missiles, poison for food/water supplies: anything to force the opponent into a limited war.
Atomic Rockets and
Rocketpunk Manifesto are both good resources on space warfare, and there are a few good discussions and essays at Spacebattles.