While cruising in Ramat Aviv today, I realized there are 3 parking types (at least), and only a simple amenity=parking tag
public parking (free)
private parking (only the building tenants can park)
public parking (payment required)
There are possibly more types I haven’t thought of, but these are important enough that we want to have a distinction between them on the map.
A 4th type I just thought about (for Tel Aviv) is:
4. Municipality owned public parking (payment required, Ahuzot Hachof, TA residents get 50% discount)
I’m not sure we may want to go that direction since the moment you start classifying it by payment type, you can have endless variation.
In the simplest you can tag it with access=private.
I sometimes use other values such as access=customers(for shop parking), access=university(for staff/visitors of the local university) etc.
Later renderers, satnavs, and other applications may make use of some access=values but generally they will not want to direct users to access=private.
So you should be able to define all parking lots with those two tags the correct way.
I would not add the amount of money you have to pay for the parking. But If you would like to add it. Put it into the “note” field, so other people can later use it somehow.