Sometimes playing a "just a" can be even worse than playing a cliché special snowflake. Keep that in mind.
It really isn't about the character you play, but rather about how
you play your character. Keep in mind these virtues of RPing that I use and should apply to any character, whether RPed as an unimportant mook or a king.
Be honest about your character; if so and so happend in their past, how would they act? What are his/her strengths? Weaknesses? Are these proportional, and do they show? Does your character feel sincere, or if not, have a valid and concious reason for feeling insincere? Is your character realistic and plausible within your own universe?
Try to provide new, insightful, or exciting ideas to the table through your character. Inspiration can be drawn from anywhere, from movies to art to your personal life to music etc, and a great character is one who embodies an idea or a spirit. Unique characters work best when they are unique not to the lore, but rather the way similar characters are played by other players. Notice other players tend to have very angsty and gritty Sith? Then play a more light-hearted one who sincerely believes in the goals of the Empire, or perhaps a cold and reserved manipulator. But that doesn't mean you should play a 1,000 year old demi-god in the body of a sexy twi'lek girl who only wears a bikini and rides a rancor. Ever.
Giving other people time to flesh out their character and be "in the spotlight" marks the difference between a mature and an immature player. Having great ideas isn't just enough; one must also share the spotlight and realize their character is not the protagonist but one of many characters. One must not just talk; one must also learn to listen
A great guide to avoid being en eye-roll inducing, cliche, unlikable, whiny, and nauseating character is the the Mary Sue Litmus Test. Every fiction writer, from RPers to novel writers, should use this as a tool.
Most of all, if your character's biggest flaw is people hate them because they are "too beautiful", "too smart", "too rich", "too lucky", or a combination of these, a serious retool may be needed.