Shooters take a bit of practice. First time you play one, you won't know the fundamentals. Just keep playing the same difficulty level and the such. What I usually do is try to pass through one level without using a continue. After I manage to do that, I try to pass the level and get a no-miss bonus (no deaths in one level). At first, you will play shooters for the means of survival. Playing for points will only happen when you can play an entire game without using any continues. Since you're playing Touhou, try to use a shift button (focus mode) to move at a slower rate, which will help you navigate through patterns a lot easier.
Do not try to stay at the bottom of the screen. It helps to be moving upon both the X and Y axis.
Oh and I'm now starting to learn how to play BeatMania IIDX, and it's a pain (I'm not used to play 7 key rhythm games, especially on a specialized controller). We're gonna be learning two different (but similar in some senses) things together lol.