And somehow, all this arbitrary stuff collided with my analytical mind. Should I make the ships move faster? Or slower? Or more/fewer of them? And what should be the next wave?

This all day. It's amazing (and frustrating) how even the simplest concepts end up with so many different parameters. It takes a lot of will power and single-mindedness (which I all too often lack) to focus on completing the task at hand without being dragged down the 'what happens if' rabbit hole.

You should be able to envision the finished game in your mind before you even turn on the PC. that vision is what should make you want to build games, not because its a cool job / fun hobby.

I'll 100% agree with this too. When it comes to designing games, the aim should be in place before a single line of code is written. I have a txt file on my phone, that when ever I have an idea for a mechanic I think will work, I just add to the list. When I'm about to start a game I then trash the concept out a little further with the aid of a trusty paper and pencil. If it seems like the sort of thing I'd want to play, that's when I start thinking about how to code it.