From an ex-military Recruiter: finish sixth form; you always need a back-up plan in case you don't make it into the Army. It's easier to get qualifications now than break off your studies and try to pick them up months later.
Otherwise, as above as regards doing your research. I don't know how long the recruiting process is currently taking, but you'll need to get professional advice on the timeline and the best point at which to apply. You'll also need a plan post-college. Selection doesn't actually take up a massive amount of time, so you need something to keep you occupied and possibly earning.
As a priority, check your medical records now, and see if there is anything that could stop you joining.