Hey cunning_stunt,
The first date is a very important interaction between two people because it will often set the impression of how interactions in the future will be handle.
Each of your suggestions will allow you to access a specific kind of information about the girl.
With that being said, it is crucial that you find out what YOU WANT from this girl? Spend 5 minutes thinking about this, and than come back and let us know. I think you will have greater clarity as to where you want to take this girl, when you understand what you want from her.
Btw, its totally normal to NOT have any clue of you want from this girl before a date. This will just mean that you might need to set up a date in which you get to find out what you want from her
Sam