I have heard lots of horror stories about renting a U-Haul. Some people hitch their car to the back of the U-Haul truck but that could make for some pretty stressful driving I think. If you're going a couple thousand miles it may make the most sense to hire some long distance movers. They can take care of car shipping too, usually. Someone mentioned earlier that when she moved from the West Coast to Madison it was around $3300, compared to her friend who moved herself for around $1000 less. That's a considerable price difference but also with professional movers you probably have more piece of mind, and you can fit more stuff in their truck so you don't have to get rid of your furniture if you're attached to it. Make sure to factor in all the costs of moving, you might find that hiring long distance movers actually works out to be fairly close to the cost of doing it yourself, depending on various factors. Just something to think about...
