You need a stable employment history anywhere that's legit. So, working as a bouncer at a titty bar or running a medicinal marijuana grow won't count. Everything else is good, as long as you are not constantly written up for being late or for doing something else stupid. Working a bank is fine, but every local department is looking for dependable people that can show up every day and do the job, going to hundreds of drunk domestic calls. Whatever insight you gain into fraud and financial crimes from working a bank is good, and all experience is helpful eventually, but won't impress anyone during the hiring process.
My department is simple - take a civil service test, and if your score is high enough, you are moved to the rest of the hiring process. You get extra points towards your test score for speaking one of about six foreign languages that are considered useful or being a veteran. Most of the time, they don't conduct panel interviews, so the only times you talk to someone is for your polygraph, your psych and your background. And none of those people care to be impressed, but only care that you're not trying to BS, have a right "profile", and don't have a shady personal or professional past.