Corellian Light Corvette
All classes in SW:TOR eventually earn access to a personal starship to transport them around the galaxy. Both the Jedi Knight and Jedi Consular classes have access to the same type of ship, referred to on the official site and in-game as the "Corellian Defender-class Light Corvette," though it was previously referred to as the "Vanguard-class," as you will see in some of the older screenshots below.
From the Holonet on the official site:
Developed at the height of the Great War, the Defender was custom-built for the Jedi Order. The Jedi Council commissioned the starship after determining that Republic military vessels were not well-suited to the Jediís more specialized missions. The Defenderís exterior design is based on the consumer model corvette, but it has been outfitted with countless customized upgrades. The starship includes two levels. The formal upper level features diplomatic meeting rooms and an elegant conference room at the shipís center. The conference room contains a unique Holocom system for secure communications with the Jedi Council. The Defenderís lower level includes a cargo hold, a medical bay, and a small private space in which the Jedi can retreat for meditation. Despite the Jedi Orderís commitment to peace, the ship is battle-ready. If circumstances warrant, the Defender is engineered with high-powered shields and twin turbo lasers to engage the enemy.
From the Codex:
During the Great War, the Jedi Order was granted use of Republic military vessels, but these starships proved unsuitable for the specialized assignments Jedi often undertake. Eventually the Jedi Council decided to commission a new corvette, custom-built for Jedi missions.
The Defender-class corvette is built on two decks. The lower deck is based on a standard keel and houses a cargo hold, engine compartment and full medical bay. Most of the Defender's customization is on the flight deck, which includes a private cabin and meditation chamber, along with a state-of-the-art cockpit. At the center of the ship is a spacious conference room equipped with a holocommunicator for discussions with the Jedi Council or diplomatic talks.
Although peace is a key tenet of the Jedi, so is self-defense. In case of hostile action, the Defender possesses a high-powered shield array and twin laser cannons.
The Jedi is awarded a starship at the end of the class questline in Coruscant, which can be anywhere from level 15-20, depending on how many side-tracks the player takes while questing.
In addition to being a form of transport, the starship is the player's home, workshop and hangout for his companions (and the player's friends, if he invites them aboard). There are also space combat missions which take the form of a rail shooter mini-game, which can earn experience and a special currency for upgrading the ship, though only through non-visible combat upgrades that enhance the mini-game; there is no current ability to customize the appearance of the ship, interior or exterior.
The ship's amenities include:
Cockpit galaxy map for perusing and selecting
Cockpit mission reader for accepting space combat missions
Secure holoterminal for communication with headquarters
Cargo hold access for extra storage
Crew confererence room with intercom for discussions with crewmembers
Workshop with crafting bench for use of Crew Skills
Personal quarters (for "intimate" discussions)
Medical bay for Doc or Theran to hang out in
Escape pod for emergency egress
Despite what the official quote says, the Jedi's personal quarters are on the upper deck, in the forward "hammerhead" section, port side of the bridge, and the cargo hold is off the main holoterminal room, not on the lower deck. There is also a door for an "escape pod" on the main flight deck, though it's not clear what this is for.