There is an entire thread dedicated to camping at Disney, just scroll down from the resorts thread to see it. That one resort has its own section & all the experts post there. Also, you will likely end up with more questions before you go & can find answers there.
That said, I have tent camped twice, once with a car & once without. I have a VERY large tent & had no problem storing bags inside bags inside my tent.
Things are as likely to get stolen while camping as they are anywhere else. That said, I've never had anything stolen while camping & don't think luggage would be a hot item to lift. Although, with anything, camping is not the ideal situation to bring 'top of the line' anything. So, if you have a $2,000 set of luggage, head to Walmart & spend $75 on a roller bag & a fee duffles & take those.
I think FW has quite helpful staff & I wouldn't hesitate one second to ask them if they can help store some items for you.
When I didn't have a car they used a large van to take me & all my gear to my site. They also picked me up at 5am to get me to lobby in time to catch my DME. All coordinated at the front desk.