Don't overthink this Dustin, just ask her out!
If you are polite and considerate, there will be no problem. The worst thst can happen is that she will refuse, either rudely or politely. Depends on the person. Coffee is a good beverage because, unlike booze, it has no romantic overtones, no legal issues, and is usually more casual than going to some bar or club after dark.
"Going for coffee" is a foot in the door, so to speak, but it isn't really a date.
Oh and BTW, "stalking" implies something predatory and violent. You could say a hunter "stalks" a moose through the woods with the intent to kill it. If a human being "stalks" another human being, his motives are highly suspicious. Hunters always hunt; they never just watch or observe. Observers are always passive.
Now that I have stake in this, I want to know how it turns out.