I've never actually tried to order an iPad through Apple.com or purchase one in a brick-and-mortar store, let alone right after launch.
When I ordered my iPhone 5s, 32gb, space grey, I ordered through my carrier website on opening day, and received it in the mail 4 days later. Some people just got their iPhone 5s a week or 2 ago, through Apple.com, while I've had mine for more than a month now.
The Retina iPad Mini is going to be extremely hot. Every single iPad Mini owner I know and have read (which is a LOT) wanted Retina more than anything. Extremely high demand + extremely low supplies = an interesting launch weekend.
My suggestion? Order through Apple.com. On release day (or night, since midnight), just sit in front of your computer in the comfort of your home with your payment info ready and wait for the seconds to tick down to the Apple Store update. As soon as you are able to, place an order for the model you'd like.
You might receive it in a week, or a month. Inversely, you could drive out to each of the 3 brick and mortar Apple stores and try your luck. If you're like me and hate lines and just simply large crowds, I'd strongly advise you against that. I don't think it's worth it. Order from your warm, cozy home, and then simply wait for your new iPad to arrive. What's one month to this whole time you've gone without one? =)
EDIT: After reading your initial post a second time, I feel that I should let you know that you are always able to actually place the order for whatever model you want. The only thing that changes is the estimated shipping time.
Good luck, and also, CONGRATS on your win!
10-26-2013 11:26 PM