What would be the best medium to print this standard on, and how should we go about transferring this design onto that material? Should we even transfer it ourselves, or should we order it? If so, where should we order it from?
If you’re strictly looking to print something, you could try an iron-on kit. You can pick up the paper at many craft stores. If you’re feeling a bit more adventurous, you could always cut the design out and glue, sew, or use iron-interfacing to attach everything.
If you get your T-shirts made at a print shop, you could ask them to screen print one, if you buy some fabric. They should already have your artwork on file, or you can give them new artwork. As for the sewing, if you have nobody that has the ability to sew something like this together, you should see if there is a shop nearby that will do it (you could even see if they will do it for free for you, in return for being recognized as a sponsor).