Subjects are irrelevant, and the prime background varies somewhat depending on the party you want to represent.
Going to Oxford or Cambridge, joining the Union (the debating society at each of those universities is called the Union) and networking like hell with the other wannabes you meet there would be a good start. Traditionally you would also study PPE at Oxford or SPS at Cambridge.
At the same time, you need to chose your political philosophy and join the appropriate party. Be active in the local association and the university association. Stand for election to your local council.
Having done all that, you'll want a job to fill the short space of time between graduation and getting selected for a safe seat (probably at the second attempt, most young hopefuls have to fight an unwinnable seat first as a sort of test). Party researcher, lawyer, or something in the media would be good, if you are a Conservative, somthing in the city would work too, but it doesn't really matter.
Preferrably you'll need to find a suitable wife/husband, partner who will be prepared to tolerate the life of MP's partner - not easy.
If you do all that, keep networking all the time, and don't express any opinions which diverge from those of your party, you have a good chance.
Alternatively, you might decide that doing all that might give you a good chance of getting selected for a safe seat, but it would also make you utterly unfit to make any kind of decision on behalf of real people, and decide instead to get a proper job, and have a real life
Worked in the House of Commons some years ago.