There are NPC shops on most Darkness or Quest worlds to buy basic equipment, but that stuff isn't terribly wonderful. You can obtain better equipment by looking through the Commerce Forum where people sell goods. Many people also offer free equipment to new players, and most factions will give new members a starting package.
You can also shop on Centerpoint Market
and the Trade Federation Marketplace
, as well as from many factions that buy and sell goods. If you browse through the rules pages for equipment you think you'd like to obtain, each item lists the factions that produce it. You can look up that faction's website in the faction list to see whether those goods are in fact for sale (most are, but some of the "fanciest" gear like Imperial or Rebel equipment are reserved to those factions) and how to purchase them.