First of all, who in the world are Mary Sue and Gary Stu?
They're the same thing. Telling you - those two are exact same thing. Let's use just Mary Sue for now.
Mary Sue isn't a monster from a faraway galaxy you have to avoid, neither is Gary Stu.
Mary Sue is a character (obviously) that is basically someone xir creator wants to be. For example, if it's a girl, she usually has a strange hair color while everyone else doesn't, or she has "naturally" weird-colored eyes, while nobody of her race does. She is usually completely perfect, everyone wants to be her friend, all boys just stare at her and fall in love with her immediately. The creator usually dresses her in a skinny outfit to show her outlines (won't do in this galaxy!) and puts her on high heels (sometimes, but how will she run, though?). She is almost never too fat, usually skinny, her lips are often descriped as plump, and when describing her eyes, author might use something like "staring into your soul", "as if can read your mind", "sapphire/amethyst/emerald", etc.etc.
So, how to avoid Mary Sue?
You probably won't have to ask this question if you are playing for a canonic character; however, if xe isn't in the book, then you probably should look here.
1. Before submitting the form, re-read it. Ask yourself - "Is my character 'too awesome'? Is xe almost perfect?"
2. Give your character some imperfections; for example, when someone is in trouble, xe is slow to react. Maybe xe is afraid of soogers (little insect-like creatures), or is unfriendly, or mean?...
3. Make them more simple. There's absolutely no need to create a character who can do everything. It makes the game more boring.
4. Ask for advice. The ones who are more experienced than you are will give you a good advice.
5. If you can't create a good non-Sue character, ask for a canonic one! There's nothing embarassing in that - even, less work for you; no need to sweat about their biography, age, personality... and the form is way smaller. Besides, some of the characters have some good stuff not all non-canons are able to get!