T-shirts are one thing. Polo becomes a whole other demon to fend off. Stay away from anything that could be construed as "individualized". Polo shirts start delving into "style", then you'll have to determine mens vs women's style and several other key issues. Been there, done that. BAD idea. Cost of the shirt is not the major concern here.
Also, students (most likely) being the ones to make sure the paperwork is right, so the little lady doesn't get the XXL shirt is pretty darn important. "Do I need to lose weight?!?!?" The idea is easy to leap from t-shirts but it isn't… Trust me. With t-shirts, 50 smalls, 75 meds, 100 large, 100 XL, 50 XXL and be good for any given function. Style is fairly irrelevant as long as it promotes the given company, or in this case WSU. Extras will go to other events and make sure there is no date on them, i.e. "2016". Run out of sizes, "Take a small and give it to your kid" and it's accepted with a smile and a "Good idea!".
To use Ed's phrase but in a different light, "expectations" would be raised considerably with a Polo shirt over a T-shirt. Trust me on this one… Not trying to blow anyone up. Just have had this exact experience.