As someone who entered the dating pool first at 18, then again at 36 (divorce), and the last time at 39 (after a 3 year relationship went bust), I can tell you that the woman's (and your) age is a determining factor. The older a person is, IMO, the more direct you can be. I'm not saying you can ask her "Hey, wanna shag?" but I also know that as I got older, the less women cared about the "opening gambit" and it was more about the middle and end game. While a "coffee" date is cliche, no matter how old a woman is, she wants to feel safe, so the first date needs to be something non-threatening and friendly, e.g. a walk, coffee, or maybe a daytime movie. OTOH, you can just come right out and ask "Would you like to go out sometime?" That way, you will know her intentions right away - if she says "no" then you are either misreading her or she is not yet ready to make her intentions clear. If she says "yes" well, you're all set. If you want to make it safer, you can ask her to coffee, a walk, or something that people do even if they are not "dating." Dinner or lunch is fine, provided it is not a restaurant that screams "Romance!" Maybe something like "I have read about a new Asian/French/etc. restaurant and want to try it...would you like to join me?" DON'T OFFER TO PAY for goodness sake. For myself, I always took the most direct approach as I got older, simply because I didn't want to beat around the bush (hoo boy...I know). Some women liked that, some didn't.
Lastly, I agree with Sun Dummy...I have lots of regrets...not for things I have done, but things left unsaid and undone. I've told some women things that I, in hindsight, probably should've kept to myself (unrequited love and all that), but at least I won't be left wondering "If only...."