There are 115 different types of ships to purchase and pilot on Core Exiles. These range from the basic starter Marauder and then diversify into various types. For a full list of all ships, see the ships category.
Every player starts out with the Marauder ship. It is limited in options, but functional and will get you around. You can later on upgrade your ship to a one more to your liking, assuming you have the credits on hand to purchase them, of course. When purchasing a new ship, you will trade in your old ship (for which you'll receive a discount), unless you have a Universal Hangar License, in which case you can decide to add this ship to your collection.
Each ship has a number of properties which distinguish it from other ships. For starters, each ship has a cargo area (which can be extended by cargo expanders), which is the maximum amount of cargo you can carry. Each ship also has a base hull strength and armour strength, as well as a base speed, which will serve you well in combat. Each ship also has a base amount of energy it generates, a build-in reactor if you will. Of course, each ship has a price as well, and you'll need to be a certain level to be able to fly one.
Each ship has two weapon slots, three system slots, two reactor (or energy) slots, one cargo expander slot, one shield slot and one engine (or propulsion) slot. These are the same for all ships. However, each type of ship comes also with a varying number of special slots and pod slots.
There are currently five vendors of player ships, for the full list see the ship stores category. You can also purchase ships from the offical store. You can then trade the ship token you received for your ship at the store that sells your ship. Do keep in mind that that still need to meet the required captain level, you will not be able to trade in your token until you do.