I imagine there would be similar strategic goals to regular warfare.
For an attacker at the most basic level there are three options: Annihilation so they're completely defeated, attrition so they lose enough things they get worn down enough to do what they wanted, and exhaustion like blockades until they eventually submit. A defender has an additional option of survival by attrition, keep on not losing until eventually the other side is sufficiently worn out and stops spending resources on the war.
Games usually focus on direct annihilation or large battles in the hope of attrition. Some strategy games may use that for a while, although I think it is mostly a tool to hold one player back while the opponent amasses an army sufficient for annihilation.
As for specific objectives, I think they lead to basically the same premise.
* Capture and return, with resources, information, prototypes, key people, and whatever else. Could be accomplished through secrecy and espionage, or a full-on attack team. The "capture" could instead be leaving something behind, or stealing/growing/harvesting resources and bringing them back. Get in, do something, get out.
* Capture and hold, often with key infrastructure. Again you could fight your way in, or slip in unnoticed. Get in, stay in until others arrive.
* Search and destroy, often with key resources, infrastructure, and key people. Similarly as above, can be covert. Get in, sufficiently break stuff.
* Blockade, prevent infiltration.
I don't think anything fundamentally changes with a "revolves around planets" game style.
In real life, interplanetary and interstellar warfare probably won't be about what happens on the ground. The biggest thing is getting stuff from one planet to another planet, or intercepting things before they arrive. If you've got enough power for rapid interstellar travel then you've got enough power to destroy a planet. "Nuke it from orbit" is a viable strategy as far as we can see, and throwing a bunch of big space rocks could be enough. A few small space rocks -- maybe the size of a house -- could level a small city. Somewhat larger space rocks, maybe a few hundred feet around, could decimate a wide metro area. An even larger space rock could be an event like a dinosaur-killing meteor that would transform the planet so much the warfare stops being significant. An attacker could throw space rocks from any direction at any distance.
At their simplest, an attacker can just fly an interstellar ship at the planet and not hit the brakes. As long as it hits the planet fast enough, the planet gets destroyed. Even if the defender breaks up the ship, if the debris hits hard enough the planet still gets sufficiently destroyed.
It does not have to be muliplayer, it does not have to be symmetric, it does not need to be balanced, it does not even need to have other entities than the player (like player vs environment). Basically free yourself from all/most of traditional restrictions 
