Nice redo of a classic retro game! I'd suggest having the left/right speed of the player ship be faster than the bullets. Nice one.
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You can upgrade the move speed of the ship :),.. just have to make a choice about what to upgrade, health, weapon fire, or move speed. Max move speed is MORE then enough (to much to be fair, tricky to nudge over small amounts :P), and at max weapon speed, you really don't want the ship being able to keep up with that :D.
Hope you give it another go, and maybe put a few upgrades into the move speed :). Feels much better after a couple. Had to keep it slow at the start to give some incentive to upgrade it.