I tend to view spaceports as more akin to commercial airports than commercial seaports. Mitchell International Airport in Milwaukee has both a passenger terminal and a cargo terminal. Passenger aircraft, upon landing, head for the passenger terminal. Cargo planes, primarily UPS and FedEx, land and head for the cargo terminal. The cargo terminal has the equipment needed to unload the aircraft cargo containers, which tend to be designed to fit the curve of the aircraft fuselage. As the aircraft fuselage is not exactly near the ground, the equipment is basically large fork-lifts capable of reaching the fuselage. Now, if you are thinking of lots of bulk cargo, then a mose specialized facility is likely going to be needed, or the ship is going to be a self-unloader, capable of unloading its own cargo.
As for landing, there you are basically dealing with the ship-dry dock question. Can the dry dock take the weight of the ship, and can the ship bottom take the weight of the ship when it is resting on it? What is the ground pressure per square inch, square foot, square meter, of the ship's landing surfaces? My ships tend to resemble flattened submarines, with fore and aft cargo doors along with beam doors, for precisely that reason, ground pressure. Passenger staterooms are above the cargo deck for the Free Traders, Tramp Cargo Liners, and Subsidized Merchants. I figure the clear height of the cargo deck needs to be at least 15 feet/4.5 meters to allow for adequate clearance for various types of cargo, both container and odd sized. My standard small shipping container is 5 foot by 5 foot by 10 feet, 1.5 meters by 1.5 meters by 3 meters, so one-half a Traveller dTon. That makes for much easier movement on the ship and allows the ship to carry its own forklifts for unloading as needed.