If there's one thing I've learned about costumes it's this: Details are everything. You can have a pretty basic satyr (or faun) with some legs (even if they are digitigrade), a vest, and a scarf, but it's not going to be particularly impressive. Having a Satyr is like having anything, you need another layer of detail. Some examples are like this:
A post-apocalyptic character
A medieval character
A Steampunk character
Each are pretty generic, and can get you as far as the basic structure of the clothing, which is why you need to add another level of detail:
A post apocalyptic trader
An elven mage
A medieval ranger
A Steampunk airship pirate
At that point you're capable of not only the structure of the costume, but also some of the larger, base accessories. Let's go another step even deeper:
A post apocalyptic trader that specializes in objects scavenged from decaying ruins
An elven water mage
A medieval forest ranger
An Indian Steampunk airship pirate
Not only is there the costume and accessories, but you now have details for the accessories and clothing as well. To go even deeper you could make an entire personality and backstory, but I don't generally go that far.
For the satyr costume we haven't worked out the details, but luckily there's a general idea for Satyrs. Chances are you're not going to see a technologically advanced Satyr so things like a ranger, rogue, mage, or shaman all work well. For something unique a blacksmith Satyr might be interesting, but a generally anything beyond that would start to look strange. A Satyr with a gun (even a blunderbuss) would look odd, for example.
The best way is to pick what you want generically, then narrow it down as you go. The Satyr costume is in the first to stage at the moment, slowly evolving into the second stage.