It’s of course hypothetical, but it would seem to depend on who the enemy is.
I would assume the first space battles would be extensions of Earth wars. In that case, you might be dealing with satellite-to-satellite combat, or some vehicle attempting to disable/destroy a space-based weapon.
Conceivably, the moon or some sort orbital platform could also be used. It’s not too far beyond the realm of possibility to imagine combination aircraft/spacecraft that operated in both environments.
Anything beyond that would either require a tremendous technological leap for us, or contact with some sort of hostile extraterrestrials. With the latter, one would hope we survived long enough to reverse engineer their technology...
Many, many years ago, I was involved with the “A-Sat” or, anti-satellite rocket engine. It was a relatively small rocket engine which could be mounted to the belly of an F-15 which would climb at a certain angle and launch it.
A bunch of us young engineers were to mount it in a test cell for firing. I asked one of the older guys what kind of warhead would be mounted when it was used. He said “none”. It was simply an inertia weapon! It only had to get in the path of its target and run into it. Made perfect sense. Satellites are pretty fragile...