Can I change the order of two of the game's phases: Buy units and Combat move? What will it change? What are the benefits?
Regarding the order of play, the game is designed so that you buy your units guessing on what you will need next turn, after the results of all the combats from now until then, including the results of your turn
What if the order of buy units and combat move are exchanged?
So the players would first make the combat moves, then buy their units.
What will it change? As long as you do it before any dice is rolled (resolving any combat) you will still have to buy according to your guess on the results of the battles of your turn, so that aspect will not be changed.
What is the benefit? More insight. For beginners and for big maps (excessive maps, actually) like 1940, the player has definitely much more insight of what he can loose and he can need after the combat is resolved.
After introducing the game to a few new players, actually just finishing a game right now :), I wanted to share this small detail. It makes life a bit simpler. In tripleA (computer game similar to this) one of the maps actually implements this modified rule.
[based on kirst's answer below]
I'd include the AA gun's combat move fire after the purchase. First place the aircraft in their destination with a die on each that passed through an AA gun, after buying units, resolve AA fire and after that resolve combat.
A list of the games that use AA fire during combat and non combat move would be useful, I think this rule was abandoned for the mos recent editions
According to some rules sets, as soon as the combat moves are declared, AA guns will fire at any planes passing through or into their territories.
If you employ the "combat move - purchase units" order, then this is a very important rule to enforce, as you will know if you need to replace any planes that will be shot down before your buy.