I'd guess this is one where individual authorities would take widely different approaches - some maybe sympathetic, others less so.
But, as Sussex says, better to be upfront rather than trying to hide anything, particularly as the vetting procedures will disclose even police warnings and the like, and not just any criminal convictions.
Of course, that's not to say you wouldn't be successful, but if there is stuff on your record then it won't help your chances if you try to cover it up, because you'd almost certainly be found out.
But at a rough guess I'd say the length of time clean will be the main factor they would consider, assuming there's nothing else significant on your application.
Maybe a good idea just to get in touch with them and ask what their likely approach would be before submitting a formal application, because it would cost a bob or two to go through the application if it was subsequently rejected.
Of course, there's no guarantee until it's actually done and dusted, but no point throwing money down the drain on an application that's never going to succeed. There are plenty of those in the news section on here
