best advice-have better pilots flying better planes with numbers on your side :) I layer my cap, using the new recruits in older planes as bottom bait. Also having read Greyjoy's AAR, I've started experimenting with using a smaller % of ac on cap, to allow others to scramble.
Assuming this works, I'm going to start setting my cap to 'sweep range 0' with 30-40% cap. this way I don't have most of my fighters away escorting raids when i really want them to protect my base/cv.
Also, if you are having trouble with enemy A/C interdicting your shipping coming to/from a port (rangoon comes to mind, and port moresby) you can LRCAP target a TF even if it is out of range at the moment, as soon as it is in range your fighters will cap it. Try sweeping around the enemy base instead of directly on top of it to catch smaller flights of enemy fighters rather than facing the entire cap, and conversely limit the range of your cap to 0-1 unless there is reason to set the range farther (escorting a strike, protecting multiple bases/TF in the area ect) Also LRCAP is fatiguing, so set a % to rest to help prevent fatigue.
On the offensive, sweeps are your friends. Try to sweep a hex before the raid gets there. Best way to accomplish this is to have the sweeping fighters closer to the target than the raid itself. Pay attention to the device database, and tailor your raids to take advantage of so called 'flak gaps' (with the latest beta flak is a lot more effective). Try having a Submarine or picket ships between your launching base and the target base to save more pilots.
I'm sure others on here can give you a lot more (and better) tips, but these may help get you started.