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You gain hypers by chaining enemies and collecting bees (there are other factors as well, it's not exactly clear how it works), when the pink bar in the upper left corner is full an hyper item will appear. If it happens while you are fighting a boss, the hyper will be automatically added to your stock and all the bullets will be cancelled into stars.
As for the ships, it depends on your play style: A-Type is fast and precise (good for long chains), B-Type is slower and has a large shot that covers almost the entire screen. In DOJ I used laser all the time, so I always chose Leinyan or Exy with A-Type. But I never really got into the game, it's really hard (with a PS2 joypad it's even worse) and I hate the scoring system.