How do you choose girls to ask out?

So, I'm a newbie at this dating game, having never asked a girl out, etc. And as a freshman in college, I realize there's still quite a bit of time out there, but this seems to be a fundamental stumbling block I'm running into, and I would appreciate your advice, Reddit.

I've been a lurker around subreddits like this for quite a while, and feel like I have a rough grip on many of the general concepts that are common themes: the necessity of eye contact and smiles to single someone out, confidence to initiate, and touch to escalate.

But in my case I get stuck at the first step. While I'm in engineering, more than a tad awkward, and probably not the best looking of guys (A short skinny long-haired ginger), I've managed to come into contact with a non-trivial number of girls that I would consider dateable. However, in initial, or follow-up interactions with any of them, I cannot for the life of me discern if they have any interest whatsoever. I've recently got numbers from a few of them, some of whom I will will be dealing with periodically for a while, so should I just take a flying leap, take one or a few out to coffee or lunch, or should I maintain a holding pattern until I run into a girl that I can tell has some level of interest?

It's only been on very rare occasions (quite possibly one) in my life that I've had girls express much of any interest in me, even looking back on my life with my (only slightly) more mature eyes, so I need an idea of what needs to happen.

TL/DR: What level of reciprocity do you look for before asking a girl out?