I personally wouldn't bring omiyage or alcohol, especially when meeting a girl for the first time. It's about discretion and trust. Some of it depends on where you are meeting her- if it's in a public place, I would say no to both. Remember that whatever you bring, she'll have to carry back with her, and providers generally don't want to draw attention to what they do. As for alcohol, it's unlikely that she's going to drink while on the job (although you never know), and it's one thing to open a bottle of wine in your hotel room and have a glass of wine together, but carrying a bottle around, or a mini-bottle of wine or sake, is more hassle than its worth. If you want to get your drink on, buy some at the conbini on the way there.
If you want to be a good guy, bring her an unopened bottle of water (you can buy this when you get your alcohol or what have you, and then you can give her a choice), and pay her for her time without her having to ask -- I usually just put the money down on a table where she can see it, and I expect neither she nor I will mention it. Other than that, just show up clean, smile, be gentle, and those are really the main things that providers care about.
Enjoy!