This is so true. The project you take on is the least important aspect to consider. First is the lab, second is your supervisor, third is money (does you supervisor have any), and coming up lucky last is the project. I don't mean to say that the project is unimportant (it is actually really important), but that as an inexperienced researcher you are not really able to pick what is going to be a good project (neither is you supervisor unfortunately). It really involves a bit of luck, but if you are working in a great lab with great people who have money then you much more likely to end up working on a great project than you are by just trying to pick what be a great project from the start.
Wow your priorities is very much the same said for startups: too much emphasis and commitment on the initial product idea (project) in the beginning and not enough attention to the possible risks coming from the team (lab), the supervisor (angels, advisors).
