The best mascots reflect something distinctive about the schools they represent. That could be an animal native to the local area or a reflection of the area's history, such as the Conquistadors or the Pioneers. (Some schools adopt the names of local Native American tribes as their mascots or use euphemisms such as "Chiefs" or "Braves," though this practice often gives rise to controversy and accusations of insensitivity.) You can also make it a clever riff on the school's name: for example, the mascot of Hamline University in Minnesota is the Pipers, while Concord High School in California is the Minutemen (despite the fact that they're 3,000 miles and two and a half centuries away from Revolutionary New England). Avoid anything too esoteric--you want it to be memorable, not confusing--but the less generic you can be, the more your mascot will stand out from the crowd.
It's possible to come up with a mascot that isn't particularly fierce, especially if it adheres closely to the school in some other fashion. (The Syracuse Orange, for example, makes a nod to the Dutch roots of upstate New York.) But in general, you want your mascot to reflect a fighting spirit, a sense of ferocity or a proud and noble figure to represent your school. Take a moment to consider the qualities your mascot invokes when you think of it, and decide if they work for you.
Before settling on a mascot, think about how it will appear at your school functions. You may need a costume, which must adhere to budgetary limitations and basic logistics. A rattlesnake, for example, probably means an expensive and unwieldy costume, while a cowboy, on the other hand, can easily be facilitated with boots, chaps and a hat. You might speak to your local costume shops and see if they have an outfit that adequately represents your mascot. Furthermore the mascot needs to appear on T-shirts, banners and other paraphernalia, often with the title of the school above or below it. Consider mascots on commonly available spot art, or make sure the artist you commission can draw your chosen mascot well. Finally, check other schools in your district--paying special attention to those which teach the same grade as you--and refrain from picking a mascot which matches any others.