When you establish your background and skill set. Specialize. Don't be a jack of all trades and stick to your skills. Don't suddenly pull out a skill just because it's convenient for your character. An Assassin is almost always overpowered this is something on the RPers side as they assume that since they are a Ninja, Assassin or other powerful character in Hollywood mythos. So don't do that..
Real Assassins are weak against direct combat. However since they sneak around communicate all of your actions however minor they are to those you plan on interacting with. That way you know what limits you have and can keep others from calling you overpowered.
Once your skill set and background is made, stick with it.
This is an excellent guide on the matter. But to summarize what undoubtedly is a long article and an even longer leap down the rabbit-hole (this person has tons of interesting pieces):
Good assassins blend in. Uniforms are a bad idea. Also a bad idea is to look like you're up to no good; so no hoods, no masks, no knives strapped to your boots and bracers.
Hoods are designed for inclement weather, so wear them only when it's raining, snowing, much too hot or much too cold.
It may seem like a good idea to cover your face, but wearing a mask lets people know that you're trying to cover your face. Immediately it raises suspicion. If you must wear a mask, have a good alias; maybe you're a leper, or a burn victim. Maybe you're attending a masquerade.
Use generic weaponry and equipment. A super-speshul one-of-a-kind hundred-year-old ultra mega awesome sword just makes you easier to identify.
Fight to win, not to look cool. This means no backflips. It also means no long gloating speeches.
Throwing knives don't actually kill people; at best they're distractions. Bows aren't very good for long-distance sniping; they were fired in volleys, and archers learned how to shoot at distances, not at precise targets. (Fifty meters, a hundred meters and so on.) If you really want to be a medieval sniper then you'll want a decent crossbow instead.
Most assassins and hitmen are hired to whack cheating spouses, asshole bosses, and other small-time lowlifes. Don't always play an Agent 47 or a Corvo Attano, killing enormously powerful fat-cat politicians.