While we're talking about resource management: start by bombing everything that poses half a threat, and see how far you can get this way. Make an effort to not waste bombs instead of an effort to win, it'll be just a test run. You'll most certainly fall short because even with Touhou being liberal with resources, you can't just bypass everything (except in MoF) - but you'll have an idea of how many bombs you should save for later.
After that, identify which of the attacks you bombed are reasonable and which are not for your current level; try to learn the less difficult ones and don't be afraid to keep bombing the ones that you just can't figure out. After a few more runs you'll have a clear separation between stuff that you just can't afford to bomb, stuff that means a net gain if you capture but not a problem if you bomb, stuff that you should be prepared to bomb at any instant because you know you have few chances of capturing it regularly, and auto-bombs for parts where trying to survive is futile.
If after that you still fall short, choose some cards you can do somewhat regularly but still bomb often, then ignore all previous advice and try to capture them no matter what. It's better than needing to capture the endgame stuff, and if you really screw up early, it's less of a pain to restart.
Oh and playing above your level does wonders. So does StB in all its glorious brutality.
