You forgot the one plane that can do all of those things better than any you listed and interdict shipping too!

The P-38 out of all war planes of the Second World War had the ability to do all of those things in spades and to a higher standard than the rest.

It was unrivaled as a gun platform, smooth, steady and had superior pointing characteristics to all other Prop planes of the war. ( This is probably the single most important aspect of a fighter plane that is expected to perform multiple tasks!) It had the best weapon installation of all allied fighters. ( Discounting the Mossy because it is not really a fighter, but an attack plane!) Early on, it's aerodynamic performance was unique, later on, other planes had some traits that were superior in one or two areas, but fell far short in others.

Based on strategic merit alone I'm going for the P-51 from the B model onwards as the best all-round fighter. It was the only type produced that gave any significant length of service, that  you can say that you could have used as a single fighter type for your entire air force in all theatres. The only fighter mission was the sorts of extremely high altitude interception missions that the later model Spitfires could perform against reconnaissance aircraft, but then there were experimental and post-War versions of the Mustang which could do that, which proves it could have done that as well if the need was there. It was also successfully tested as a carrier aircraft, but again there was not a need. Finally it was significantly cheaper than any of the competition, which matters a lot in the context of getting the most out of wartime resources.

However, the B model Mustang only arrived in late 1943 so it is only fair to consider a couple of contenders for their total length of service as top tier types. In the ETO the Bf-109 served for the longest period if you include pre-war service, from mid-1937, and with upgrades could mix it up with later types right until the end, so considering it served for more than three times as long as the B+ Mustangs it could also be considered for the title of the best if length of service. The Spitfire came into service a year later and the Mk-I and Mk-II weren't quite as good as the Bf-109, in overall performance with the two bladed prop and then in armament and diving ability, but the Mk-V and the 109F were on a par and many consider that the Spit was better after those models, so overall the Spit was pretty even with the 109 in the ETO for the title of "The Best", if length of service is considered.

Neither Spitfire nor the 109 was/would have been comprehensively useful in the Pacific so that needs to be considered separately. On that count I rate the P-38 as the best, as its because it served from just before Pearl Harbour until the end of the Pacific War. In the Pacific it's range and twin-engine reliability outweighed the performance imperative and cost considerations of the ETO and with upgrades it could do the same or better job as any of the later types in that theatre right until VJ Day.

So in summary "The Best All-Round Fighter" might be considered to be:

1. P-51B on overall strategic usefulness.
2. Bf-109 and Spitfire for the ETO if length of service is considered.
3. The P-38 in the PTO if length of service is considered.

I know I'm going to get arguments about the P-47 being the best for it's survivability, but the fact is that it couldn't do all the required missions to be considered an all rounder until the N model in 1945, which I reckon is too late to count. It was also no interceptor whereas the Mustang could concievably do that job adequately with the right modifications.