Fighting mid air battles is defined by the technology you are using. Air combat between Zeppelins is going to be far different than air combat using modern jet fighters.
For large and slow moving vehicles, air combat will resemble naval combat. The vehicles will be relatively immobile and combat will be joined by using cannons, rockets, missiles or whatever other sort of weapon system is employed in the scenario. The ships will essentially be large firing platforms. Many steampunk scenarios (and illustrations of hypothetical air vessels before powered flight was common) followed this trope. While helicopters have not been involved in dogfights, it is probable that helicopter air combat will also follow this format.
World War one fighter planes were defined by their relatively low power to weight ratio and slow speeds. This limited their weapons to rifle calibre machine guns and allowed for fairly tight aerobatic manoeuvres.
By WWII, aircraft were much faster and more powerful, and capable of carrying much heavier armament, including .50 cal HMG's and 20mm cannon. While still capable of doing the manoeuvres of their WWI ancestors, the increased speed meant that a much greater amount of airspace is needed to do the same thing.
Jet aircraft generally no longer fly and fight using the same sorts of manoeuvres as their propellor powered ancestors, and indeed, now that missiles can manoeuvre with far more G force than any human pilot can hope to survive, air combat is more a contest between computers, electronic countermeasures and other technology. There may be some circumstances where jets are in visual range and could dogfight so many modern jets use thrust vectoring or canard airfoils to provide an edge if and when they get into that situation. The Russian Sukhoi Su-35 epitomizes this sort of thinking, while the American 5th generation fighters are optimized for using sensors and electronic warfare to fight without getting too close to the enemy.
So define what sort of setting you will have, and the technology that is being used, then the answer to your question will become clear.