I'll be perfectly blunt, and this isn't to 'bash' you, this is to situate you properly. The CF is not a dumping ground for those lacking the judgment to make it in other careers.
As a matter of policy, all legal obligations must be discharged before your application will go anywhere. This will likely include sentencing conditions such as any period of probation. If you 'beat' the charge as you put it, the CF cannot discriminate against you in terms of employment, though it's possible that it may still affect your application for MP. The MPs are, after all, a police force. You must prove yourself to be possessed of the maturity and judgement to be entrusted with the role they fill even here at home.
If you are convicted, then you are a convicted criminal and will have a substantially harder time getting into the C.F. MP is out, as is undoubtedly medical officer. The recruiting for Med O is a different thing altogether anyway, but I cannot conceive of the C.F. taking someone who's just gotten a DUI and paying their way through med school. Firefighter is also very hard to get into directly, most (if not all) people getting in are transfers form other trades. I do not imagine you would be competitive with no military experience and a recent criminal conviction.
Past whatever mandated waiting period there is post conviction you will still, with a criminal record, be competing for any job with those without one. The C.F. attracts a lot of recruits, and the doors aren't exactly open these days. Put it this way: if a civilian police force, firefighting organization, or medical school wouldn't take you under these conditions, why should the military?
That's not to say you will not be successful in getting into the CF at all, but you've named three trades that range from somewhat to extremely ambitious. Check with the recruiters, but also realize that your judgment will be distrusted for quite some time to come. I would hope, frankly, that with our recruiting intake being as limited as it is that you would not be considered competitive for several years at least. Play it straight and prove to the military that you deserve a spot. If convicted, you'll be starting with a hell of a disadvantage.