When playing against the Axis AI, you can shoot down a lot of Axis fighters in 1943 through air superiority missions over the Ruhr, using massed P-47s at 28,000 ft (or even higher) early in the week; you can then have them escort bomber missions later in the week. When you get P-51s, do the same thing deeper into Germany, but adjust the flight path of the A/S mission so that you "make a tour" of Axis airbases with large concentrations of fighters. You can do something like this with Spitfires, although the AI generally moves its fighters to bases beyond Spitfire range by late 1943.
General notes on Allied fighter altitudes: the game seems to do a decent job of mirroring real life capabilities. Spitfire V - 15-20k ft, Spitfire VIII/IX - 25-28k ft, Spitfire LF IX - 18-22 k ft, Spitfire HF IX - 25-32k ft, Spitfire XII - 10-18k ft (this is a real beast at low altitudes); Spitfire XIV - 22-28k ft, P-39/P-40N - 8-12k ft, P-38 - 18-28k ft, P-47 - 25-32k ft, P-51 - 25-30k ft.
I use P-38s in the Mediterranean to provide long-range A/S missions over invasion task forces and beachheads, until I can get Spitfires/P-40s into captured airfields. I use P-38s/Spitfires to provide the same sort of protection over French invasions and the Channel; if you don't do this you will suffer shipping losses from Axis naval air patrols.