Well, the external details of the different variants of F4U are pretty minor. One would have to be a real nerd to to really even notice given the limitations of tattoo artwork... I love it!

The most common would be the F4U-1A. Although, it should be noted, the designation -1A was never officially used. It was applied post-war to differentiate mid-to-late production F4U-1 Corsairs (those made from mid-1943 onwards) from the earlier ones. (i.e., it's not an "official" variant). The main visual difference between the F4U-1 and the F4U-1A is the cockpit canopy. The first Corsairs had a robust "birdcage" canopy. To increase pilot visibility, the canopy was redesigned to a simpler two-frame design without all the framework in the way, and the pilot was raised up 7 inches. Other aesthetic differences include a small (very small, like six inches long) stall strip (a small triangular prism shaped "bar" attached to the leading edge of a wing) on the right wing, just outboard from the gun ports. Also, the -1As were fitted to carry a drop tank under the fuselage.

The next major variant of Corsair was the F4U-1C, which first appeared in August 1943. This variant swapped the six .50-caliber machine guns for four 20 mm cannons. Only 200 of this variant were made. They were built in conjunction with the F4U-1D. The -1D was a fighter-bomber variant, featuring fixed rocket tabs and bomb racks, and twin belly drop tanks. This variant didn't see service until mid-1944, though. Compared to the F4U-1/-1A, the -1D had a more powerful engine. Also, the cockpit of the -1D was further modified to a single piece bulging design, further improving pilot visibility.

The last variant from WWII was the F4U-4. This variant entered service at the end of 1944. It had an even more powerful engine, requiring a scoop under the nose. Also, it sported a new 4-blade propeller and --once again-- a slightly updated cockpit, this time with a flatter windscreen. There's also the F4U-4C, which swapped the machine guns for four 20 mm cannons. These were much rarer, though.

Other much rarer variants of note include the F4U-1P photo reconnaissance variant, and the F4U-2, of which only 32 existed. These were F4U-1s modified to replace one of the machine guns with an airborne radar These served as carrier-borne night fighters starting in 1944.

As for your bombers, the B-24 would be perfectly historically accurate. I'm assuming you're wanting a Corsair from either the USN or USMC from the Pacific Theater. Well, the USAAF flew B-24 Liberators in the Pacific theater throughout the entire war. Their longer range and heavier bomb load compared to the USAAF's other premier long-range bomber, the B-17 Flying Fortress, was considered an asset in the far-flung islands of the Pacific. In fact, the B-17s were phased out of Pacific service in the middle of 1943, leaving the Liberator as the dominant heavy bomber in the Pacific until the B-29 was introduced in mid-1944.

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Edit: Oh, you might also run into the F3A Corsair and the FG-1A and -1D Corsair. The US military at the time would use different designations for the exact same plane built by a different company. F4Us were built by Vought. An F3A was just an F4U built under license by the Brewster company, and an FG was built by Goodyear. They were all identical to their Vought-built counterparts. (except for the Brewster ones. Those were plagued by shoddy workmanship).