I usually recommend that people get the qualifications they want before joining the military, so you have a fallback career option if you don't get through selection. There are a lot of stages that are pass/fail, some allowing you to reapply, but the medical could rule you out completely.
Staying in education also allows you to develop your leadership potential through participation in societies, sports and uniformed organisations.
It is possible to do a degree through remote learning once you're in the services, but it is a big commitment, and not easy when you're still getting established in your role and if you're on detachments and deployments.