Terry Tao has some helpful ideas.

I don't think can't say I've really mastered the practice of choosing problems. I know a good answer guess if there's an area of math that you're really familiar with, questions will just start coming to your questionyou, but I can't tell how much of that ability comes from some osmotic process from the examples of peers.However

When I'm stuck, Terry Tao's blogI try to write down where I am in a lot of detail, then I take a break. If I'm lucky, I know what sort of knowledge might be able to crack my problem, and if I'm even luckier, I know who has some helpful ideasthat knowledge.

I don't think I know a good answer to your question. However, Terry Tao's blog has some helpful ideas.