Dating is essentially about moving into the other person's personal zone and sharing both the time but also life together - you are probing each other and finding out things about the other person to see if you are a good match for a life together.
What you do in that time together will reveal if you are compatibel - if you both enjoy museums, then do that. If you both like concerts, do that. Do not be shy with what you like and try to show the other person a slice of your world, but do not overwhelm them with yourself and what you alone think - the life is meant to to be shared and therefore it must be balanced.
You won't be compatible on all levels and all people have their individual quirks, but it is the sum of the compatible elements that will sway you towards being with that person.
It is good that you want to avoid sex until you get really serious, as this shows an expectation of a deep emotional investment and maturity, and it makes sense in a way where men and women pair-bond during sex, which is only enhanced if you know them very well.