Ladies- a question about respecting women in public?

I'm confused as to how women want to be treated by men in public. I'm 24, decent looking and i generally like myself. I'm not sure what the best policy is when it comes to relating to women in public. On the one hand, I feel like avoiding looking at them, trying to keep conversation to a minimum-to-nil level and generally only interacting with them on a need-to basis is respectful because it demonstrates that you're not "that guy" who hits on women in public, yet on the other hand I feel maybe women want to be acknowledged as individuals, and perhaps they're shy, hence why they don't come off as being very open. I'd love to casually chat with females, but as I said, I don't want to be "that guy" or a creep. I've spent my whole "working life" (8 years) in public service and have seen my fair share of that. Any advice is appreciated. Cheers!