So you want to play a satyr?

First off, I applaud you for playing something that is not a standard D&D race! Unless you played Changeling: The Dreaming, you probably never saw "satyr" on the list of standard characters races before.
At the end of the day, satyr characters are not that different from human or elf characters and most character archetype could be adapted to a satyr relatively easily.

female Poseidonous satyr by Zeta Gardner

Satyrs are best known for their libidos and a lot of players like to play flirtatious or promiscuous characters. That's fine as long as your game master and the other players would not offended or annoyed by this. This is a good thing to check over with your gaming mates in Session Zero.
That said, you don't have to play a satyr if you want to play a promiscuous character. Humans are not exactly very chaste and elves, gnomes, and dwarves all have a few lusty individuals among them.
Also, you don't have to play your satyr as a one-dimensional sex fiend. Satyrs in folklore embody more than just carnality. They also embody a love of nature, music, and art. They value wisdom of all sorts and revel in physical challenges. Even if a satyr is not ruled by his/her libido, it is very rare for satyrs to be passive or shy. They are not stupid or reckless (necessarily), but they are not likely to talk or wait when the situation calls for action.

Satyrs don't have a true homeland to speak of, but like gnomes and tengku they are generally well used to assimilating into the societies' of others. They also have their own subcultures within the societies' of others so it is good idea to figure out what ties to other satyrs your character has if any.
While most satyrs love learning and more than a few like books, a satyr is unlikely to be happy cloistered in a library forever. Cerebral satyrs exist but most satyrs seek to balance their mental actions with physical actions and most of a satyr's racial abilities are physically oriented.
The satyr's alertness bonus is useful to all character archetypes. The Willpower penalty rarely comes up, but it when it does the rolls are very important indeed. Besides the hefty cost in freebie points, that is a satyr's only true weakness, but you can compensate by putting extra dots in Willpower at character creation.

Satyr Herd

Comissioned Male Poseidonous Satyr by Zeta Gardner

When a satyr says "satyr herd" they use the term as a synonym for "satyr ethncity". You should probably figure out what herd your satyr character is a part of. You can even make up a new satyr herd if one of the existing ones doesn't meet your needs.
Note that most satyr herds in Scarterra are spread thin over a wide geographic area and satyrs are highly individualistic, so your satyr character does not have to conform to your herd stereotype in anyway if you so choose. Also, satyrs mix and mingle in both senses of the phrase so you could easily play a satyr with a mother and father from separate herds. All that said, here is the nonexhaustive list of satyr herds in Scarterra's northern hemisphere.

The herds below all have at least a couple thousand of members. Scarterra is dotted with smaller cultural herds that make up between 20 and a couple hundred members such as the somewhat infamous Mountain Goats of the Border Baronies. Thus, if you want you can make up a brand new herd for your satyr character if your game master is willing, and if the game master is me, I would be happy to work this out with you.
Codenya satyrs, nature loving satyrs closely allied to wood elves and assimilating their values.
Confederate satyrs, minority satyr population found throughout the Colassian Confederacy
Faun satyrs are a pacificist leaning minority population within the land of Kantoc.
Kionus satyrs, barbarian satyrs roaming the cold northern region of West Colassia.
Mediterranean satyrs, earthy agrarian satyrs commonly found in the eastern inland region of West Colassia.
Poseidonus satyrs, sea loving satyrs that commonly work as sailors or set up homes in coastal regions.

So you want to play a warrior who is also a satyr?

Satyrs have a bonus dot of Stamina (and the potential to buy a six dot rating) which is handy for any warrior. Maybe it's not as handy as a bonus dot of Strength or Dexterity, but Stamina is nothing to sneeze at. A high Stamina means your warrior is are harder to poison, harder to knock down, and less likely to fail a Fatigue check.
If you are the sort of player that wants your warrior to use parkour stunts in combat and otherwise fight in a flamboyant fashion, a satyr's enhanced speed and Athletics bonuses will come in handy. Also because your character can outrun most other characters on foot, you can chase fleeing enemies or flee pursuing enemies that much easier.
Otherwise, a satyr warrior is not going to be very different from a human warrior. Satyrs do not have any culturally favored weapon so your satyr PC can specialize in any weapon or fighting style that you wish.

Comissioned male Mediteranean Satyr by Zeta Gardner

So you want to play a Rogue/Expert who is also a satyr?

by Me with Hero Forge

A satyr is a good thematic fit for a sexy and somewhat chaotic rogue archetype that is good at sneaking around and running away.
The Athletics and Alertness bonuses are handy for any scout or sneak-thief character archetypes.
Satyrs don't have to be dexterous rogue cliches. Satyrs value wisdom, so you can justify a satyr who is an expert on almost any subject matter though you are unlikely to see many cloistered academics. Any satyr scholar is going to want to balance time in the library or laboratory with field work and real world experimentation which is well suited for most RPG campaigns.

So you want to play a mage who is also a satyr?

by me with Hero Forge

You can justify a satyr mage of almost any stripe. A plurality of satyr mages are Folk Magicians, but satyrs can be found practicing every variation of wizardry, plus an occasional sorcerer and more than a few Warlocks.
Whatever their base tradition, it is common for satyrs to practice the bardic interpretation of their tradition. Of course, a player character satyr doesn't have to be a bardic caster if the player doesn't want that.
Any school of magic can be justified for a satyr mage. Players can devise satyr PCs however they want, but NPCs satyr mages are more likely to be jack-of-all trade magical dabblers than they are to be top of the line specialists.

From a min-max perspective, the school of Conjuration and school of Invocation primarily use Stamina as the casting attribute making it a good choice for the optimized satyr mage.
Since they are physically oriented, the School of Transmutation is a good thematic fit. The school of Enchantment can be a good thematic fit too, though a lustful character that can bend people's minds may be dark and mature for some players. It is noteworthy that given that satyrs themselves are more vulnerable to mind bending spells than non-satyrs, many satyrs consider it a grave taboo to violate another's person's will via magic. Satyr enchanters tend to be found among the most conscientious and moral enchanters and also among the most vile and depraved enchanters.

So you want to play a divine magic caster who is also a satyr?

Player characters are often the exception to the norm, so your satyr theurgist PC can be affiliated with any one of the Nine or be a member of the Cult of the Compact even if it is not common for satyrs of your character's herd to do so.
Comparatively speaking, satyrs priests and theurgists of Nami are very common. Satyr priests and theurgists affiliated with Korus, Zarthus, and Maylar are fairly common.
Satyrs affiliated with Mera, Greymoria, Greymoria, and Cult of the Compact are known. Satyrs affiliated with Hallisan, Khemra, and Phidas are rare to the point of being practically unheard of.

comissioned portrait of Aleesia the Satyr by Zeta Gardner

Male Kionus Satyr by Zeta Gardner

Satyr theurgists are likely to default to the favored spheres of their affiliated deity, but Plant, Animal , and Weather work well with a the satyr race's general love of nature. Augmentation and Wrath are good fits from a satyr's stereotypical direct action focus. Divination is a good thematic fit with their keen senses and love of wisdom.
Satyrs are unlikely to use divine magic hiding in the back casting spells from a distance while other people are doing the fighting, so Necromancy , Spirit Magic, and Hexing are a bit out of character for most satyrs, but they are not impossible.
Necromancy, Weather, and Purification all use Stamina as a base attribute making them good choice for a satyr theurgist from a min-max perspective.