So I am slowly becoming better and better at getting numbers from girls via cold approach and day game.

Now, for the last girl I did this with I right away told her that I want to invite her on an actual date and told her to give me her number.

Which she did.

Now...how soon should I message her to arrange the details (place and time)?

I don't want to seem overly eager, but if I wait too long she will just forget me, so I have to strike the iron while it is hot and I'm still in her memory.

What is the rule of thumb for these cases?

Also, do you generally text or call?