This you mean moving Aircraft?
For Aperture Priority, camera must be set above 5.6 which give you enough head room for dept of field.
For Shutter Priority, camera must be set above 800 to capture fast speed. Higher speed requires more light so set the ISO to 200 or higher is needed if your picture is dark, unless you post process the picture later.
It's hard to shoot pictures in full manual if your subject is moving, especially in an uncontrolled manner. If subject get's into different lighting condition, so are your settings.
I suggest you try mastering between the two priority settings and move to full manual control once you know how to shoot proper settings on your camera. Even pro hardly use full manual control unless they’re doing fancy imagery. In most cases the movement is controlled.
Thanks for your advice on which settings to use - I'll try them out.
I didn't realise that - I just assumed that I might get a better shot if I manually tweaked the settings. I see what you mean about it being hard to switch to the best settings while tracking a moving object though. I do have priority settings on my camera so I'll use them for now.