Long range bomber escort: P-51D
High alt interception of unescorted bombers: P-47D or Bf 109 G-10
High alt interception of escorted bombers: Me262
Anti-shipping missions: TBM / Ju88 / Ju87
Short range dogfight: Yak9U
Airfield attack: P-47D / F4U-1C / Typhoon
Infantry Support: P47D / Typhoon / F4U-1D
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Nothing beats the Pony for range.
Focke Wulfs (excepting the D-9) are notoriously horrible at high alt performance. While the venerable 109 may lack the firepower of an A8, it climbs to alt much quicker and is more maneuverable at high altitude than the FW. I also chose the P-47 because of its superb high altitude performance and toughness. While not my choice for a "scramble" defense vs high alt buffs, were it already at altitude there is not much that could outrun it up high, and 8 x .50 cals would be more than effective.
To intercept bombers in formation you need speed and big guns to do the work fast and in as few passes as possible. Even moreso when there are escorts about to make the work more hazardous. The Me262 has the guns, and the speed, but even it cant compare to the combination available on the 163. I did not choose it because I wasnt sure I could trust my memory on when it first saw service (I was thinking early '45). If it was available in '44, then it would be my choice hands down. *Note that no limit was put on the question in regards to amount of service seen or numeric availability, only the plane choice for the job.*
The Ju87 has obvious limits, although if interception is not an issue, the Stuka performed this service admirably early on. The TBM is recognized as the king of the torpedo bombers for its speed and lethality in delivering its payloads. The Ju88 is often overlooked in an anti-shipping role, although it is outfitted with torpedos. It's a little large for a torpedo bomber, but it does have good speed and good coverage from its rear guns. Given ample diversion for AA by fighters, the Ju88 could easily deliver a deadly blow to a carrier group in formation, and its gunners could well defend it against attacks by fighter cover.
Short range, given the ability to rearm, nothing beats the Yak9. In the right hands it can turn with the spits, run down Focke Wulfs and even Ponys under the right circumstances. It's fairly tough for its size, and its guns are lethal (though the numeric lack and low ammo counts require good gunnery skills and the ability to rearm in an extended fight). It's small size makes it a small target, and it has a good ROC and good speed despite its lack of WEP.
Airfield attack and Infantry support I go with the same planes, only excepting which version of the F4U I choose for the different roles. The -1C is more useful in base attacks, as its cannons are more useful vs hardy targets, while the -1D is more available, and the 6 x .50s more than adequate for troop support. The Hog and the Jug are chosen for obvious reasons. Both are tough, fast, haul unbelievable amounts of ordnance to a target, and make very stable gunnery platforms. The Typhoon also is very underrated in AH for its ground attack capability, for which it was most famous. It's rockets are specifically designed AP rounds, and its 4 x 20mm Hispanos are deadly to anything that gets in front of them. Only its low ammo count and short range (and less available ordnance) make it secondary to the American iron.