The biggest determining factor was which service you were affiliated with.

Marines were sent almost exclusively to the Pacific theater, due to their focus on amphibious warfare and the island-hopping nature of that fight.

Since both major theaters involved a significant ocean voyage, the navy was involved in both sides, however aircraft carriers were stationed largely in the Pacific, so Navy and Marine aviators and support personnel were largely sent to the Pacific, not Atlantic.

The Army and Army Air Forces (USAAF, the precursor to the USAF) were both predominantly sent to Europe, although divisions were sent to the Pacific, South Pacific, and North African theaters as well.

Not to forget the forgotten service, the Coast Guard was mobilized and served in the Atlantic, Pacific, and North African theaters as well as sent to more exotic locations like Greenland

When Divisions and other units were formed, the troop quota for each division was filled with Enlistees and Draftees. The draft was a randomized lottery system. When you enlisted or were drafted, you were trained and subsequently assigned to a unit based on your personal skills (good shots went into infantry, mechanics went into armored etc.). They could also volunteer for specific roles such as the Airborne. If you enlisted, you enlisted for a specific branch. The Marines only accepted volunteers. Formed units were moved into armies as they were needed. If your relatives were both regular army it is partially their individual skill sets, partially their unit readiness, and mostly random chance in their draft dates where they were assigned.