My preference would be for F-86F Sabres or F9F-8 Cougars. I wouldn't go with any FJ-3/4 Furies because their J65 engines were more finicky than the Sabre's J47 or the Cougar's J48.
Both were AIM-9 capable, and they used the same ammo as the US forces' .50 cal & 20mm aircraft guns, thus keeping them shooting long after M61 cannon would be out of ammo.
Both were also pretty maneuverable, and could carry WW2-era bombs.
Their engines also were designed for early jet fuel - which was similar to kerosene, thus they could serve4 with then-current fuels.
Plus the F9F-8 was carrier-capable, even if the arresting gear & catapults would be at their limits and might need upgrading.
Yes... even though you said munitions would be sent back as well, they really would likely be able to use up all of what got sent well before the end of the war.
The same goes for repair parts... everything they needed was within the capabilities of WW2 fabrication facilities, techniques, and skills.
Additional aircraft and engines could also be made, expanding their effect on events.