My university issues a t-shirt too! Last year it was a deep V American Apparel one and if it's the same design this year then I'm planning on wearing a very thin gold chain with a very small charm. The necklace is almost choker length, with the charm laying kind of in between my clavicle. I'm planning on pairing the shirt with a pair of J. Crew chinos (they're on sale online now!)
Is your shirt like the Alabama recruitment Comfort Colors one from last year? I don't remember exactly what it looks like but I don't know about wearing any kind of necklace with a pocket tee. Kendra Scott is a very popular jewelry designer in Texas (I actually know her - she's a very sweet lady!) and they make really trendy earrings and long necklaces.
These might be a bit "basic" but they're still a good way to jazz up an outfit for a decent price:
http://m.kendrascott.com/danielle-ea...not%20provided
http://m.kendrascott.com/fashion-des...-necklaces?p=1