Pave the driveway, carport later - procedure?

I can already see, no matter how you do it, there seems to be no right or wrong.

No one can make the decision for you.

Another question: Often the roof covering is offered with steel trapezoidal sheets or trapezoidal sheets with a fleece coating. If I read correctly, the fleece coating would be better because there is no drip cave. Opinions on this?

You can save on the coating for a carport. There is hardly any risk of a drip cave. It looks different if you integrate a storage room (tightly enclosed).

Rainwater would probably just be collected in a rain barrel.

You can save on the gutter. Unless you need the rainwater for the garden. Water is a valuable resource.

Is a flat roof of the carport usually sloped only to one side (back) so that rainwater can drain, or sloped to the side and backward so that you have a central lowest point, otherwise gutters would have to be installed on both long sides if the slope goes only to the back, or ...?

Note that the concrete surface should also be sloped at least 1%. For the roof at least 2%. Where you drain depends on the surroundings and the property.

we bought it painted, not bare metal

I am aware of the roof's slope, but the concrete area is new to me... and now of course I'm curious what this is all about ...