My two cents (from the female perspective):
Lunch is always a good idea - doesn't imply a date, you can meet there rather than picking her up, allows both of you to escape after an hour if it's awkward, and can segue into a dinner date.
I'd personally hold off on the flower until you graduate to a real date. The flower (which will be a hit at the right time) implies you want to date. Women often like to go slowly, and like to spend enough time to know if they are comfortable enough to see you in a more date-like setting.
Asking her: Just say, "Would you like to get together for lunch sometime?". She will know it's a way to get better acquainted. If she hedges on being available, no big deal - she may be involved, not interested in dating, whatever. If she says yes, follow up and contact her to set a date and time. If you don't, you'll come across as a player. Word gets out about those guys.
Ask what sort of food she likes, or if she has a favorite place. She will love your consideration.
Always call afterward (next day) or even email to thank her for the time you spent together.
Never ask a woman at the last minute - it implies she has nothing better to do.
Movies are not the best place to 'get acquainted.' too dark & you can't talk.
When you finally go on the 'real date,' if you plan the place & make reservations (if needed), she will love it. Women love guys who can make plans.
Don't scrimp on the tip (and don't wildly overtip). If yo scrimp, she will wonder if you are a cheapskate. Too much, and you're insecure & trying to be flashy. Tip appropriately for the envoronment & the bill.
Open the car door, take care to walk on the side of the street, and otherwise display good manners. You'd be surprised at how many guys ignore basic manners.
Just a few thoughts - good luck!
Sossy