the easiest route from a programming standpoint would be to use full/individual animation's for each move/attack/injury's, usually you'd use a sprite sheet and write a small animation class to select the appropriate frame of an animation in the sprite sheet, and play it.

a more complicated route, but one that can give much nicer results(and would require much less artwork), is to use a skeletal system for body control, and you would have multiply sprites representing individual body parts, these parts would be rotated with the bones, and you could then author animations with the skeletal system, and not require unique sprites for every possible animation. however this has it's drawbacks, joints require a bit of special handling, since you might get stretchering of the mesh at joint points(usually solved by placing a slightly larger joint texture at these points, to cover up any potential eyesores). you can theoretically extend this system to use rigid body mechanics to get more realistic reactions to a fighter being hit.

it's up to you for what you choose to use though, both methods have been used in big name fighting games, so either one has been proven to work nicely.

For a question posted in the For Beginners section, I'd say go with full body sprites. A skeletal system is not necessarily "better". I imagine making sprite animations the traditional way is easier for sprite artists, and also programming using full body sprites is easier. Given the power of today's machines, even low-end ones, the advantage in resource usage for a skeletal system is almost irrelevant in normal circumstances.