Wtf... speedos? We were issued navy blue, mid-thigh length, average swim trunks. No speedos, no civi bathing suits.
All that fancy-shmancy poly-pro stuff for running is unnecessary, I find. I made the mistake of not bringing white cotton socks, so for the first 4 weeks or so I ran in grey cotton socks underneath the standard issue wool socks (the cotton socks 'cause I can't stand the itching from the wool). It really wasn't that bad and running in standard cotton socks didn't affect me negatively in any way.
A good pair of running shoes is key, which I brought. The ones they issued me were crap, but I had to take them. They were the old, grey shoes with the foam mid-sole and orange bottom. I tell you, having messed up feet in the military is hell - the boots don't fit properly, they can't issue you any running shoes but the crap ones I got, and any medical exam of your feet or ankles will inevitably yield a shocked expression and a "um... uh... is that normal for you?" response. I had severe club feet as a kid, repaired with surgery, so my feet are strangely shaped - high instep, incredibly huge arch, very wide foot, but a size 8.5. Needless to say my balance isn't spectacular with my height being 6'2". I got jacked up for having my boots tied too lose until they realised that bulge halfway up the laces was actually part of my foot busting out of the boot. The expression of horror on my sgt's face upon this realization was priceless. He took me straight to the QM to get a different pair of boots but alas, I already had the best they could do.