Drinking:
Mormons aren't supposed to drink alcohol, because the Word of Wisdom prohibits it. They also aren't supposed to drink coffee or tea because it prohibits hot beverages, too, but they don't panic when they see people drinking coffee.
Mormons, like people in any other religion, vary greatly in their adherence to the doctrine put forth by the church--partly because nobody is perfect, and partly because some people only view the doctrine as a set of guidelines, and they make their own decisions about how to live. It is remotely possible that she will feel very anxious and upset if she sees you drinking. (My best friend in high school burst into tears once when a friend of her dad's drank a beer in front of her.) Then again, maybe she's devout in the daytime, but a hellraiser after dark and will drink you under the table.
Family acceptance:
Some Mormons frown upon their children dating non-members. Others don't really care, especially if they see the relationship as simply casual dating. Proposing to this girl would be another issue entirely, but you're not ready for that just yet, right? I don't know how old the two of you are, but "devout" Mormon families don't usually let their young daughters go on dates unless it's in a big group. The cut-off age for that is offically 18, but if the girl still lives at home, her parents may still be nervous about one-on-one dating, especially when the guy is a non-member.
But as with any situation, there isn't one rule of thumb that automatically applies to every Mormon family. I know families who are extremely strict until their daughters leave home. I also know some who give the girls free rein because they trust them to make the right decision in any situation. Some hearily disapprove of letting their kids date non-members, because they feel that they might be a bad influence, and some don't mind at all because they think associating with people who have different beliefs is not only not bad, but important because it will make the kids have a deeper appreciation for the things they've been taught.
You could get in really good if you go to church with her sometimes. Even if you don't believe a single damn thing they teach, you will at least learn a lot about what she believes.
Kissing on the first date:
It's age-dependent, but I don't think this would be a problem, unless by "kissing" you mean you plan to swab her tonsils and grope her. Keep it short and sweet and polite.
Let us know how it turns out!
Incidentally, in response to diamond:
While not all Mormons are judgmental, a few of them make up for it by being more than judgmental enough for everyone else.
Is there anything in particular you'd like to know? 
