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Okay, got the date, shes not into studying and so on. So I want to take her on a coffee place at my campus, its quite nice and not so expensive

. I thinks its also nicer than some random coffee shop in town. Shes coming by car so no big drinking.
How far should I go for the first welcome? Directly kiss on the lipps for the beginning or shall I escalate slower again?
And afterwards? Shall I try to get her to my house? Its like 10 mins away.
By the way, how is it in Sweden with paying?
Well first of all I'm not entirely sure about what either of you two want out of this relation. I will therefore just assume that you two want to possibly start dating each other.
Don't greet with kiss on the lips. This is just a date to see if you want to see more of each other. If everything goes well you can kiss at the end. However, I see the kiss more of an investment or a confirmation of you two going to meet again. It isn't necessary. With a girl I dated I didn't kiss close until third date - took her virginity on fourth of fifth. My point is that the kiss doesn't affect how you two are going to want to see each other again very much. A kiss at the end of a date is always good though.
I wouldn't try getting her to your house. You should leave after a while for something you have to do (preferably 5-10 minutes before she has to leave). Even if all you want is a fuckbudy then your first meeting can be to see if you're worth each others time (this is playing it safe though). Lets assume Styles logic: a woman won't want to sleep with you until you've spent 7 hours with her. I find that this number is actually very accurate. Changing scenery after a while can be good. She shouldn't think of you as a boring guy who'd spend hours in a coffeshop
On the subject of payment. In Sweden it is a very big focus on equality. I've never dated a woman who wanted me to pay for the movies or whatever. So I usually split the bill. I always insist of paying though, I´m yet to not be refused. However, I'm only 17 and I've heard that this changes in later years.
Example: Last night I went to the movies with a girl. I told her I have free tickets (my father gets like 500 movie tickets each year) so I would pay for the movie. She then said she felt so guilty that she had to pay for snacks. This has happened as far back as I can remember with every girl I've taken to the movies.