Be sure you are not confusing the prices listed on the rules page with actual market prices; the rules only display the production price. Faction-specific ships like Lambda Shuttles are typically not available for purchase at all, and when they are, they are very expensive. For more information about prices and trading, please consult the Trading section of the Guide, linked at the top of each page.
The shop facility located on starting planets is open to all, and by speaking with the shopkeeper you can purchase a few different types of inexpensive items like knives and staves. Please note that combat is not yet implemented and as such you may want to hold on to your money until you can purchase something more useful. Otherwise, you should be able to enter the shop facility by being adjacent to it, and accessing Position -> Travel -> Enter.
Commerce centres, on the other hand, are not NPC facilities; they are owned directly by players and you must be granted access by the owner to enter. They can be used to buy whatever assets are available on the NPC market (accessed via the Market link on your right panel).