I don’t think modern Rangers hold significant advantage over WWII rangers. I think they would actually be a detriment, as the WWII rangers were familiar with the technologies available in that time period. Those modern rangers do carry more radios than the entire invading force had during D-Day. But, any base you send will have plenty of radios to issue.
My first thought was Norfolk. They’ve got enough ASW assets to stop the U-boats that were decimating the convoys. Yeah, they won’t be able to rearm modern weapons or repair/replace certain damaged systems, but with the U-boats out of the way, the original fleet would have been much more successful. Even after the modern weapons are exhausted, the C3/ISR capabilities of the future fleet will greatly enhance the operations of the past.
My second thought is Wright Patterson AFB, home of the US Air Force museum. Designers get to tear apart aircraft that wouldn’t be built until after the war, but not so advanced that they exceed the past nation’s ability to produce. They get turbine engines 4 years early, and figure out all the transonic effects thet kept them from breaking the sound barrier. Turboprop-powered heavy bombers, flying higher and faster than anything the Axis can throw at them. Turboshaft powered submarines, destroyers, PT boats, helicopters, tanks
Third thought is to skip straight to the endgame and try to accelerate the Manhattan project. It might be a bit of a stretch to call it a “military base”, (and it’s not on the list above) but we could send them the Savannah River site. They get more plutonium than they know what to do with. With enough plutonium, they can afford to drop demonstration bombs in unpopulated areas of both the Asian and European theaters, possibly without needing to bomb Hiroshima or Nagasaki. We can avoid the need to invade both Japan and Germany.
Any base we send would have modern computers and some programmers. The German Enigma code could be brute-forced in a matter of hours on a modern computer. That alone is going to shorten the war in Europe by months to years.
Jet fuel is basically kerosene, which was invented in 1846 and available from refineries long before diesel (1894) and gasoline (1892). Refineries were producing fuel that jets could burn long before jets existed. Most military aircraft can burn diesel or ordinary kerosene if jet fuel isnt available, they just need to be careful to avoid gelling, which can occur in the cold air at high altitude.
GPS is needed for a certain degree of precision in standoff weapons. Without it, they have to rely on laser or TV guidance, or dead reckoning. The ring laser gyros and accelerometers they use in their inertial guidance systems are far more accurate than the guidance systems used aboard V1 and V2 rockets, which were themselves surprisingly effective.
GPS is not required for navigation of manned aircraft: they can rely on terrestrial radio beacons or dead reckoning with their own inertial navigation systems.
I can’t think of a weapons system that actually requires Internet access.