As someone who went to college across the country, I found that shipping a couple boxes via FedEx using a discount available to those with eBay accounts. The discount was 30% off cross country ground shipping IIRC. No need to measure or weigh the box, just put a shipping label on it and ones CC will be billed 2 weeks after shipping.
If possible, buy items there. Walmart, Target, and Costco have locations throughout the US.
For checked luggage, I'd use a rolling duffel bag as I needed to take it different places and didn't need to sign the damage waiver required when checking a cardboard box.