Can I get some advice on a couple things?

Heya all, I'm new here, and I basically am wondering how I should be perceiving this situation i'm in. I'm 19, and a sophomore in college.

First of all, I'm one of those shy guys. Although I'm doing much better lately with that :D. Also, except for an online relationship that was pretty good for a while, I haven't really had much success in dating. I'm especially bad at asking girls out and reading the signs.

Basically, I'm on between-semester break right now, and I ended up going on this school-sponsored trip a week ago to a local retreat for a few days of fun and reflection. I ended up meeting this girl there. She's really sweet and there is just something about her that I find very attractive. She also seems like the shy type as well.

We ended up talking a bit during the trip, and it turns out we both are looking into the same major, had a very similar college experience, and had very similar interests. Even more reason for me to like her. We have a class in common next semester and she wanted me to join a tennis club with her as well, so we ended up swapping numbers.

So, basically I want to ask about two things: First of all, I'm curious as to how I should be reading these signs. During the trip, there were a few times that we had brief eye contact, and most of those times, she suddenly smiled for a brief moment as well. Plus, she seemed to laugh at my jokes a lot, though I was being uncharacteristically funny and confident and outgoing for once, which i hope sticks. Also, I know thanks to one of the icebreaker games we played there (long story) that she was attracted to someone there (a point she also subtly pointed out to me later that day). Also, during a talk on college relationships, she seemed to be looking at me a lot, although I was directly across from her, so that might be nothing. Finally, we ended up in the same group for bowling, and she was always the first to high-five for a spare/strike or support if I sucked. However, there were also times on the trip where we sat near each other and nothing happened, and its not like she went out of her way to talk. I mean, I know there is simply not enough info yet to make a judgement for sure, but I'd love to get opinions on this.

Second of all, I at least want to go through with asking her eventually just for kicks. I plan on sitting next to her and talking to her in class Monday and seeing if any other signs of interest pop up. Plus, we'll probably form a study group together, so I can talk then. But, how long should I wait before officially asking her out and giving it a try? How long would be wise? I was thinking maybe seeing if I could grab lunch with her Monday or Wednesday and maybe hang out here or there and then try asking her out after a couple weeks or so if our encounters went okay. Is that taking it too fast though? I don't want to be impatient, but there is something about her that really makes me want this to work before its too late.

Also, on a side note, would maybe asking her out on Valentine's Day be a smart idea? There is always the secret crush thing the school has on that day, so that day could already be a make/break kinda thing.

Sorry for the very long post, and thanks in advance for the help.