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I would suggest that, if you can't afford to frame the shirt behind glass, that clear plastic could be stretched over the shirt. If you like the 'raw' look with the shirt exposed to the air, I would apply several layers of Scotch Gard, allowing each layer to dry before wetting the fabric again. This will make it far easier to clean, more resistant to humidity or splashed liquids; and, in most cases, will make the colors and logos really pop out. Because inks can vary, you may want to test the Scotch Gard on a leftover scrap- and don't saturate the layers. Just spray until the cloth is damp, and that is enough.
How to Make a DIY Chameleon Mug