Most races are locked to F2P accounts; they only get Human, Cyborg, and Zabrak IIRC. However, Preferred and Subscriber accounts get more options depending on what class is selected; different classes have different default races available. (For example, Miraluka can only be Jedi classes by default, while Sith Purebloods can only be Sith classes by default.)

If you play a character to level 50, you unlock that character's race for your legacy, meaning that any new characters you create on the same server can be of that race. Alternatively, you can pay 600 Cartel Coins to unlock a race, or buy the unlock for credits on the GTN from someone who paid those Cartel Coins. Since the Cathar race is unavailable by default for all classes, the only way to create a Cathar is to buy the unlock from the Cartel Market. (You can also pay 500k credits to unlock Humans or 1m credits for any other race directly through the legacy system; I'm not sure if this includes the Cathar or not. Either way, it's usually cheaper to buy the unlock on the GTN, since they usually go for a few hundred thousand credits.)

Human and Zabrak work differently, since they're available for all classes by default. Getting a Zabrak to 50 allows access to both Republic and Imperial appearances for Zabraks, which otherwise look starkly different across factions, while getting a Human to 50 grants extra Presence (a stat boosting the strength of companion characters) to all characters on the server, which is useful for low-level characters but not that great later on.

Most races are locked to F2P accounts; they only get Human, Cyborg, and Zabrak IIRC. However, Preferred and Subscriber accounts get more options depending on what class is selected; different classes have different default races available. (For example, Miraluka can only be Jedi classes by default, while Sith Purebloods can only be Sith classes by default.)

 

If you play a character to level 50, you unlock that character's race for your legacy, meaning that any new characters you create on the same server can be of that race. Alternatively, you can pay 600 Cartel Coins to unlock a race, or buy the unlock for credits on the GTN from someone who paid those Cartel Coins. Since the Cathar race is unavailable by default for all classes, the only way to create a Cathar is to buy the unlock from the Cartel Market. (You can also pay 500k credits to unlock Humans or 1m credits for any other race directly through the legacy system; I'm not sure if this includes the Cathar or not. Either way, it's usually cheaper to buy the unlock on the GTN, since they usually go for a few hundred thousand credits.)

 

Human and Zabrak work differently, since they're available for all classes by default. Getting a Zabrak to 50 allows access to both Republic and Imperial appearances for Zabraks, which otherwise look starkly different across factions, while getting a Human to 50 grants extra Presence (a stat boosting the strength of companion characters) to all characters on the server, which is useful for low-level characters but not that great later on.

To expand on this, Twi'leks and Cyborgs also both have customizations that are locked to class/faction. If you unlock the race then you get all of the customizations however.

For Twi'leks this is skin color (Sith Twi'leks get red skin with black markings as an option) and for Cyborgs it's different cyborg pieces of metal to stick on your face (These vary on class - troopers, agents, BHs, smugglers, and Sith Warriors all get different options). Once you 'unlock' the race (by paying or getting to 50) you can use any of these customizations.

You play a race to 50, and you unlock it. This means you can create a new character of that race, even if it's the opposite faction. Blue Twi'lek Sith Inquisitors, Chiss Jedi, etc.

You can also buy this unlock with cartel coins; that way you don't have to play the race to 50 first, it just becomes available for the next character that you want to start from scratch.

You can also change race for your current high-level character in the appearance modification device on your capital world. Costs cartel coins to click "apply changes", but you can switch your race to anything that you've unlocked, as above.