"Given our current technology and potential near-future technology, what would a future space battlefield look like?"
Given Current Tech Available:
Machine Guns, Guided Torpedoes w/ HE or Nuclear warheads, primitive rail-guns, primitive heat lasers, ground to low earth orbit booster rockets, small space shuttle, Soyuz capsules, communication satellites, ground observation and control, remote drones, micro-satellites, primitive Project Thor, IIS
Current Space Battle:
The goal would be to control cis-lunar space (between Moon and Earth) and would be the first battlefield of WWIII. (I can't see a scenario where the whole world puts up with someone trying to grab space for themselves.) Mostly orbital combat, with possible sub-orbital pop-up strikes. Booster rockets would launch guided torpedoes with High Explosive fragmentation warheads (steel clouds of death) at enemy targets (likely fragile communications/spy satellites) and disable them without needing a direct hit. The ISS would be turned to swiss cheese. Low Earth Orbit's space junk problem will become exponentially worse. Combat Shuttles could launch, but they would be sub-orbital or perhaps one orbit at most. The counter move to maintain a satellite presence would be to use micro-satellites to replace one large one with many "disposable" ones. All the while a crazy Electronic Counter-Measure war is going on in space to deny communications entirely and would not discriminate between military and consumer channels. Forget calling across an ocean as the world will have to fall back on copper wire or glass fiber. Eventually, it spills-over to Earth conventional war or even Global Thermonuclear War. The winner, if any at all, will be decided on the ground. The space war's most important impact will be that if one side actually does achieve cis-lunar space-superiority, the loser will be somewhat blinded and may be scared enough to start lobbing nuclear weapons around out of fear of the winner's ability to set up a Project Thor and bomb with impunity. I don't see people in space fighting it out in capsules or shuttles as they may not survive launch and re-entry without actually going into a battle.
Near Future Tech:
Machine Guns turrets, Guided Torpedoes w/ HE or Nuclear warheads, primitive rail-guns, primitive heat lasers, ground to low earth orbit booster rockets, small space shuttle, Soyuz capsules, communication satellites, ground observation and control, remote drones, micro-satellites, primitive Project Thor, IIS, Moon Base, Space Station at Lunar L1, L2, L3, L4, L5, Space Marines in primitive Power Armor, Lunar Tanks, fighting robots, Lunar artillery.
Near Future Space Combat:
The goal would be to control Earth Orbit, The Moon, and Lunar L1 through L5 and would be the prelude to Solar War I. Not sure that it will contain Global Thermonuclear War as I assume it will take global cooperation to get this far. Perhaps a limited exchange if it were a few nations making a power grab. Given the issues with radiation and micro-meteorites at the Lagrangian points, the stations would naturally be well shielded against fragmentation warheads. The stations themselves would likely be prized possessions. (if not, they get nuked using large booster delivered warheads from Earth) The Lunar Colonies would also be prized, so I would assume that nuking them would be a last-gasp "FU" from the losing side. There could be small fleets of space shuttle like warships that have machine guns or auto cannons for primary attack with the ability to carry a limited number of small guided torpedoes with frag/HE/nuke warheads. I would imagine that these craft would be well heat shielded for earth re-entry so heat lasers would have little to no effect on them. Battles between fleets would be long looping orbits with combatants sending fire at close approach moments possibly days apart in low earth/lunar orbit and even weeks apart if in high slow transitional orbits. Machine gun turret fire could be used as a point-defense against torpedoes if detected in time. Shuttles could then dock at a Space Station or possibly enter from a breach and start to fight it out corridor to corridor on the station. Or they could blockade the station.
Lunar surface warfare with Space Marines could be pretty intense as I imagine it would be the only way to crack into an enemy colony, assuming direct drop-ship approach is defended against with guided torpedoes and machine gun turrets. There would be Lunar Tanks, supporting robots (likely rover type deals with weapons), artillery fire support, drop ships, forward bases, entrenchment, support from Shuttle strikes away from colony defenses. The Marines fight their way next to the colony, likely on top of it as it should be mostly underground. Then breach the colony and begin the invasion. They would have to stay in the suits as the first defense would be to retreat and depressurize the surrounding tunnels. If successful, they would slug it out tunnel by tunnel. I imagine you could lay siege to the colony, but I would have to think that it would be somewhat self sufficient for at least O2 and Food. Perhaps starving the colony of solar energy from the surface and denying resupply from orbit could work in time as they use up consumables.