"A Mary Sue (sometimes just Sue), in literary criticism and particularly in fanfiction, is a fictional character with overly idealized and hackneyed mannerisms, lacking noteworthy flaws, and primarily functioning as a wish-fulfilment fantasy for the author or reader."That doesn't mean your characters have to be likeable, however. In the end, it should all boil down to relatability. I am not suggesting that your characters have to match up with the likes and dislikes of the reader, but give them flaws, bad habits. Make them human. We relate to that which we understand, what we can sympathize with. A perfect example: I was playing a game where the main heroine was a huge Mary Sue. I hated her, and she was borderline ruining the game for me. Then, a scene was shown where the character got jealous. So jealous that she got angry. It completely caught me off guard, and suddenly my hate melted away. I actually felt bad for her. She had shown a human quality that I related too. Sad to say, it was the only moment in the game where she exhibited such behavior, and she quickly transformed back into her one dimensional state. But for that brief moment, she was a character who I still didn't like, but wanted to know more about.
Flaws seem to be the easiest way of making a character three dimensional. Have them bite their nails, give them a horrible temper, make them horribly antisocial. Small quirks make somebody interesting, and not just story fodder. I recall, when I first starting writing my novel, I wanted to create a character for exactly that. Plot fodder. However, as I wrote him, his mannerisms and quirks surprised me. When the time came to it, I realized he had suddenly become an integral part of the cast. I couldn't get rid of him.
Characters can make or break your story (most of the time). So, unless you have a very specific idea in mind, I highly suggest taking the time to plan them out. To at least give them a foundation of a personality. Then, you can let the rest write itself.