Be a hard-charger. Be up-front about your debts and be proactive in paying them off.
Having the DUI is not a death sentence if you're honest and you demonstrate that you are the right person for the job.
If you really feel like being a nuke is the thing you want to do, there is nothing you will lose by giving it the best you possibly can. I entered in with debt and was given clearance with only a minor inconvenience. A friend entered in with a DUI, and though he can't be an officer, he is still excelling as a prototype student because he puts his mind to it, and excellence has its own rewards.