You need at least an undergraduate degree, but lots of people stay on to do a masters or PhD. I agree with Johnny, do the subjects you enjoy and don’t let people tell you ‘there are no jobs’ – there is always a way to do what you enjoy, that really is the best way to have an enjoyable career 🙂
There are quite a lot of ways into science. You do usually need a university degree (although I’ve also seen a couple of people move into science who learned engineering within a company first). But at least in my field of science (brain research), you get people with degrees from lots of different fields – psychology, philosophy, social studies, engineering, physics, maths, biology, medicine… A lot of the skills you learn in your studies (problem solving, analyzing any type of data, writing up your results clearly) are pretty transferrable, so if you’re not going too far from your field (say, from physics to political science), you can often move ‘sideways’ into different topics and apply your skills to them, or carve out a place between topics for yourself.