I think you will see a whole host of variations of starports and how each system prefers/demands that traffic within it operates. There will be at least some generic guidelines across all systems, but specifics are going to be up to each system and their ability and/or desire to enforce local regs.
On the idea of ships having to physically dock with a port, I think you'll see ships that will hold in orbit waiting for a customs cutter to come by just as often as you'd see a ship physically land - especially so for a ship that might transport down it's own cargo, or it's just passing through and not needing/wanting to dock anywhere. Again, many possible variations here.
I came up with this as sort of a checklist of activities. Obviously timing and such will also vary depending on a ship's needs, it's captain and it's crew willing to put up with such rules. A free trader with a crew of PC's is going to operate differently than a corporate-owned ship, or even a military one. I tried to keep it generic so that it's not specific to either a high port or a down port.
I) Arrival Activities
Prior to jump arrival
1. Beginning within the window of earliest estimated jump arrival, crew begins minimal staffing rotation on bridge, engineering and weapons stations (if applicable)
2. Minimal crew manning remains for all stations until arrival in real-space.
First hour of in-system arrival
3. All crew report to duty stations immediately upon arrival
4. Begin scanning local area for nearby traffic
5. Establish contact with orbital control and transmit identification data, cargo and passenger manifest, download local traffic data, shipping paths and local sensor data.
6. File flight plan with traffic control for preferred destination. Engage drive and head to planned destination.
7. Begin downloading electronic mail, local market data and in-system news.
8. Request contact/rendezvous with customs if required.
9. Allow passengers/crew to transmit personal messages to planet/system data-net.
Remaining flight time (variable)
10. Continue transit to destination.
11. File preliminary out-bound flight plan, estimated departure date, estimated available cargo space and available cabins with appropriate agencies.
12. Arrival at destination, clear customs and immigration as required.
II) Port Activities
First 24hrs of arrival
1. Disembark passengers (high & middle), deliver mail and priority cargo.
2. Revive and disembark low-berth passengers, arrange for pickup of cargo destined for arrival at port or speculative cargo that buyers can be found for.
3. Begin cargo unloading
4. Cargomaster begins looking for new cargoes (bulk, speculative, mail).
Day 2 – 5 (assumes 7 day stay in-system)
5. Begin refuel/repair activities.
6. Crew shore leave rotation begins
7. Steward begins looking for passengers
8. Begin pre-flight checks, begin loading bulk cargo.
9. Crew shore leave rotation ends.
48 hours prior to departure
10. Obtain updated flight/navigation information and charts.
11. File preliminary flight plan with traffic control, request departure slot.
12. Begin loading remaining cargo, low-berth passengers
13. Load shipboard supplies, food, perishables
24 hours prior to departure
14. Board middle, high passengers
15. Load mail & speculative cargo
16. Complete pre-flight lift-off checks
Last two hours prior to departure
17. Confirm departure window with traffic control
18. Load high-priority and any other special cargo
19. Seal ship and begin pre-liftoff tests
20. Liftoff!
- III) Departure Activities
First hour after Liftoff
1. Clear immediate area around departure port
2. Contact in-system traffic control and request departure course for jump
3. Man all stations for outbound departure (engineering, weapons, bridge)
2nd hour after liftoff & onwards (variable)
4. Begin maneuvering towards departure point
5. Finalize any last-minute data transmission to/from planet or stations.
6. Scan jump area to verify no ships or objects in the immediate vicinity
7. Power up jump drive
8. Notify traffic control of imminent departure
9. Jump!