Mascot costumes don't have to have elaborate, cartoonish costumes in order to be effective. You can use theatrical or custom-made clothing in school colors to show off the spirit. These are usually done in an over-the-top fashion, with the colors brighter, the clothing exaggerated (think really big cowboy hat, for example).That is the ultimate goal of the mascot: to get the attention of the crowd. That's why the vast majority of school mascot costumes are much bigger, flashier, and more complicated than just a spiffy outfit.
By far the most easily recognizable part of a school mascot is usually the head - an over-sized caricature of whatever character your school is represented by. Even "human" mascots like cowboys will often get a cartoonish head just to make the mascot more recognizable to the crowd from the bleachers. The head is usually made out of a combination of metal, plastic, or fiberglass framing covered by foam rubber and durable fabric. Because school mascots are supposed to be active and moving a lot, they are made to be very tough and durable, but that also makes them very heavy and cumbersome - the cheerleader inside the costume will need a great deal of practice moving around both to figure out the mechanics of it and also to build his or her endurance and upper body strength.
The ability to see out of a mascot costume is usually very limited, and the best "heads" will also have a fan inside to help keep the mascot cool during the hot games on the sidelines. It's also usually hard for the person inside to either speak or hear, and so exaggerated motions and talking through mime is another part of the skillset for a good school mascot.
The Body of a Mascot
School mascot costumes are usually full-body affairs, with the same theme set by the head (a tiger, eagle, whatever) carried through the rest of the costume. Taking a look at vendors such as CheerEtc's "cat" collection, all of the costumes are emulating the fur of the felines, sometimes with a different material setting apart the belly, or an anthropomorphized version with a stylized version of the school uniform on as well.
The shape of the body underneath the costume is a factor in both how your mascot is seen by the crowd and also in how hard it will be for the cheerleader to move in it. "Fat Suits" or "Muscle Suits" are basically padded under-outfits that help bulk out the mascot and keep the cartoonish exaggeration consistent.
Feet of Fancy
The shoes of a mascot are arguably the most important part of the costume - not necessarily because of how they look, but because they need to work. With all that bulk on top, having sure footing - that won't slip or let the ankles twist - is essential. Many mascots take the prudent route of just using cheer shoes or other gear, but there are also companies like FaceMakers that produce custom-designed footwear that is durable and good looking.
Your school mascot should also budget for accessories - not just fun things like props, but also practical items such as Star Costume's cooling vests or a loudspeaker system that can let the mascot's voice be heard as well.
A school mascot costume is much more than just a fancy Halloween costume. Spend the time planning and purchase from a quality company like those above, and your school mascot will be a great part of every school game.