-Assuming you'll be driving to San Antonio, consider taking anything particularly valuable with you in a POV (e.g., Grandma's sterling silverware).
-Technically, you are supposed to let the packers box everything up. In reality, if you already have something boxed up, they're not going to un-pack and then re-pack it. Remember that, in general, you will box something up with greater care than they will.
-Watch what they pack. I've PCSed before to find my old garbage in a box.
-Be a stickler about annotating pre-existing damage on the manifest and specifying details for expensive items. It's not a TV; it's a 42" Panasonic color plasma HDTV. Reimbursement for lost and damaged goods is difficult enough already. Without the proper documentation, you're hosed.
-Provide lunch and have plenty of cold drinks on hand.
-I'm forgetting a ton of tips that I'm sure others will fill in. Also, if you're starting residency in June, then how can you be pre-medical?