I've gone over spaceguns, and spacegear, and spacetactics, but yet to touch on martial arts. Even with the advanced technology needed to claim a place as a race capable of space combat, martial arts will still be required. No matter how far technology advances, spacecraft are cramped, and every possible inch of space is packed with vital equipment. In addition, ships not reinforced for combat may be susceptible to arms intended to pierce other space combat suits.
Which brings us back to The Old Fashioned Way. Grapples, strikes, and melee weapons, wielded by and against people likely clad in suits able to withstand the horrors of space. Obviously, things can't be done just as usual, because all you'd get is people uselessly thumping each others armor until one of them got tired or overheated; much like how modern soldiers are trained with an emphasis on grapples rather than simply breaking themselves on armored opponents.
Further complicating things is that pesky lack of gravity, either completely, or merely reduced during planet-side operations or in artificial partial G environments. A substantial amount of effort will likely need to go to further refinement of techniques that function in such conditions.
Grapples, without gravity, will be problematic. Certain techniques such as the armbar may still continue to function as they use a combination of the victim's and aggressor's bodies as the surface against which the arm is wrenched, but without some manner of magnet boots or similar technology to allow for bracing, throws and such will tend to just leave both combatants drifting apart. For unarmored/unsuited combatants, a grapple fight will turn into a very floaty series of attempts to perform chokes or wrenches and resist same.
Similarly, lacking grav boots, striking becomes near useless without something to push off of. Almost all power in a strike comes ultimately from the ground, and blows thrown with only muscle power tend to be lacking. With sufficiently rigid surfaces inside of the ship, combatants may be able to kick off walls to launch themselves into attacks, which is flashy, difficult, and risky. One would be reminded of kids in a bouncy castle attempting to fight. Any combat suits would by necessity have at least concentrating strikers, like those of a glass breaking hammer, and an emphasis on blows to the chinks in the armor and breakable vital components such as the faceplate or pack.
The last chance is the melee weapon. Humanity has augmented his might with tools ever since the first stick was lifted as a bludgeon, and there's no reason we should stop now. That said, we may need to put in some further development to tools that have largely stagnated due to alternate technologies. Like the knights of old, piercing power and ability to target weak spots will be key, but further development may be needed. Exotic materials that we're on the brink of unlocking, such as blades with a boron carbide coated superfine edge, will keep the humble bit of steel relevant; still, further exotics may be required. Vibro weapons are presently mere science fiction, but supposedly boast superb damage and armor penetration if they work anything like we imagine they might. Weapons able to generate some manner of superheated edge are more feasible at present day, as plasma cutters and such are known quantities if we can miniaturize the functional bits, at the cost of greedily burning oxygen even if they only fire during contact and penetration. Such weapons are also viciously effective if they can penetrate to the inside of a pure oxygen suit, but unusable on pure oxygen vessels. Another known quantity already well on its way to miniaturization is powered weapons, such as the chainsword and buzz axe so favored by certain sci-fi licenses. Power tools are well known entities, and while dedicated tools may be wielded against the haplessly unarmed, for use as true weapons further refinement is required; we must bring them in line with the myriad of arms humanity has developed to work with our form factor, and adjust them to suit the rigors of battle. Still, even with suitable weapons to permit damage to be done, fighting with weaponry will require some combination of grappling and striking, with the same difficulties as are mentioned in their respective sections
Ultimately finding what works will require a great deal of testing, and as always, will only be undertaken by the most forward-thinking of military thinkers, with the rest playing catch-up after they discover they are no longer fighting the last war. Still, physical combat and melee prowess shouldn't be discounted, even as we extend our reach to the stars. With sword in hand, we shall rise to the heavens.