Hmm. This is an interesting question. I don't know why I find this rather difficult to explain, but I do. But here's my two cents.
I think, to 'like' someone, you have to accept them as they are. That, of course, includes not only the things that you like about them, but also the frustrating, infuriating things that they do.
I liked someone back then, but that must've been just a combination of appreciation, admiration and a good dose of infatuation, I think. I always wanted to talk to them, to see them, be with them. When they leave the room or are not in sight, I felt deflated, as if when they left, they took away my energy. When they are there, or when they come back, I was just absolutely ecstatic.
The thing with when I like someone is that I always like the personality, not the way they look [though admittedly, if they look great, that's a nice bonus]. If I ever did 'like' someone because of how they look, it never lasts very long, and I wouldn't even call that 'like', more 'crush'; probably weird terminology, but hey.
As for whether or not I'm feeling then thinking or thinking then feeling, I don't really know. I'd like to think I'm both because I don't like going into things without knowing what it is, or where it's going. I just like being in control. However, like everyone in here has already pointed out, it really can't be controled, that liking. In engaging, I'm probably thinking then feeling, but when I'm in the relationship, I'm most usually feeling then thinking, though thinking is still there of course. It just took a backseat in a sense.
:::I figured out why this was difficult for me to explain! Heh. Because I was trying to separate liking someone and loving someone because for some odd reason, they were in the same place when I read the question- they're not of course. More often than not, I guess I like the possibility of the people. Their ideals rather than their real selves, and when I see the real selves, I get disappointed and turn away. :L