Hint: Fast Freaking Research
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Research is based on the amount of times a stage is cleared in the story or training modes. Although you can do this stage-farming trick with any stage, the easiest (and fastest) one is the second training stage.
After you escape Japan with (or without) Admiral Tsukagi, you can speedily research your tech tree by repeatedly finishing that second training stage with a fast (60 knots or better) ship, since you only need to destroy the three radar stations and escape to the south map.
Alternately, if you're inclined for even faster finishes, you can repeatedly destroy the Archeopteryx with a ship completely devoted to anti-air combat on automatic mode (on Very Easy or Easy). You can even skip picking up the parts from the boss and withdraw from combat immediately after the boss is destroyed.