What starports come with a high port?
According to GT:Starports (p. 60) :
Almost all [Class A] and [Class B] starports have an orbital facility. Most [Class C] starports at TL-8 and above will have a high port
How many [MCr] invested over how many years does it take to upgrade a D to a C, C to B, B to A??
This is a difficult question to answer. (again) GT: Starport specifies building times based on the size of the port, not the type of the port. Port sizes are based upon traffic through the port. You can see the calculation of port size in the trade map data in the wiki. Look at the "Port" column. The book gives the example of Mertactor (Spinward Marches 1537), which has a port size of 6. Based on the size of the port (a high port and down port), the whole facility is about GCr17, and would take about 2 years for the locals to build from scratch. Other examples gives a port size of 4 around GCr1 and port size of 5 around GCr6.
Calculations for building, or upgrading, a port include TL of the world (lower TL worlds don't have resources to build ports as efficiently, so the process takes longer). World population (importing workers is expensive and time consuming). Capacity for the High port (if there is one at all) vs. down port vs. underground port (for really bad worlds).
Chapter 5 in GT: Starport gives a really detailed look at the whole process.