All these questions are best directed to the OSO, part of their job is to make sure your prepared. But in attempts to answer it, you will have a wall locker and a foot locker to store your military gear in. All your civilian trash will be stored in a room that stays locked. Personally, I was a boot whore, I showed up with a set of Bates lites Jungles, issue jungles, and two pairs of Cadillac’s (the Vietnam style leathers). They were pretty specific with the way you display the boots, so a few pairs stayed in the shed with my civilian trash. You just have to develop the initial confidence to ask the instructors permission for the key to trade out a pair of boots.
Your line of thinking sounds pretty logical to me. There should be an issue sheet that states what was issued to you, if you had a pair issued, but forget to bring them for Srs then the expense will likely come out of your pocket. If you found a pair on ebay or something, I would bring them – worst case scenario they end up in the storage room. OCS is a lifetime experience, if you drop an extra few hundred on boots and socks you won’t feel to badly about it by the time you make it to TBS.