Welcome to the discussion board and to the A&A hobby!
Regarding your question, here are some thoughts:
The three operational-level games – D-Day, Battle of the Bulge and Guadalcanal – are fundamentally different from the more conventional A&A games which encompass either the whole world or one of the two major theatres. So the impression you would get of the game if you started with one of those would be rather misleading.
A&A 1914 is also an oddity because it focuses on WWI rather than WWII and because of peculiarities like its multiplicity of dice.
In terms of the WWII A&A games which are currently in print (which in general may have the benefit of being more affordable that out-of-print games, especially rarities like Anniversary), you have five options. In increasing size and complexity they are:
1941
1942
Pacific 1940
Europe 1940
Global 1940 (which is Europe 1940 combined with Pacific 1940)
1941 is designed as a starter game for new players, so it’s the most accessible game from that point of view. But you might also consider jumping straight to 1942: it’s a fuller gaming experience than 1941, but much less complex than Global 1940. Pacific 1940 and Europe 1940 are playable on their own, but unlike 1942 they’re not global in scope. So all in all, 1942 might be a good compromise choice.