When we moved from California to Missouri we started planning it three months in advance. I'd recommend that you use a professional moving company - it worked out the same price as moving all the stuff in a UHaul, with the advantage of not having to drive a UHaul cross-country.
The cars could be expensive to move. I'd recommend looking at hiring a trailer to pull one behind another, and then either ship the third (about $1000) or have someone else drive it. Of course, if you're not up to the cross country drive, you'll have to ship them all.
Don't use small moving companies. They may look cheaper but they generally aren't as professional, won't carry as much insurance, will more likely strongly debate any insurance claim, and will probably ask for a large sum of money up front. You shouldn't be asked to pay for anything in advance - otherwise they have your money, AND all your stuff. Not much motivation to arrive on time (or indeed at all). Get at least three quotes, and be careful to check the parent companies. Most companies belong to Allied or Mayflower so you may end up getting several quotes from effectively the same company!
Be sure to get a "not to exceed" estimate. This means they'll come out, check out all your stuff and give you a maximum price. If the weight then exceeds the estimated weight, you pay no more. Make sure they include any estimated "shuttle" costs if you're in a hard to reach area. If one company says you need a shuttle, and another doesn't, then you probably need a shuttle. If you then go with the company that said you don't, then expect them to add on to the quote (shuttle fees are carved out of the "not to exceed" ).
You have the right to be at the weigh station both before and after they weigh your stuff. Make sure the driver is either in or out both times. A dishonest driver can over inflate the weight like this. This is especially important if you don't have a "not to exceed" quote.
Anyway, if I can think of any other pearls of wisdom, I'll let you know.