As a former Ryder (now part of Budget) and Uhaul dealer, my suggestion is to use Penske.
I was a Uhaul dealer at one of my business locations for 6 months in the late 90's. That was abotu 5 1/2 months too long. I have noticed their equipment has improved lately, but I would be weary of trying a long distance move with them.
I was a Ryder dealer at my other location for many years, while they were part of Ryder as well as after they went independent, and after they sold out to Budget. They used to be a wonderfully run company, but IMHO, are not nearly as good as they were. Budget does has a
AAA discount and is listed in the Post office change of address packet.
I would favor Penske at this point.
Try calling to a couple of Penske dealers to see what you can get for rates. Also, try picking up the truck on a Monday as opposed to a Friday and see what that does to the rate.
If you are using a tow dolly to pull your car behind, please do NOT fill full of stuff, its not designed for the added weight.
Make sure you make a stop every couple of hours for some rest. If you are a night owl, consider driving at night when there is less traffic to contend with both as obstacles as well as congestion. If you do not function well at night, please do disregard the comment about driving at night.
Watch your speed and allow plenty of stopping space since a truck will take 9 times or more the stopping space of a car.
Drive careful and have a safe trip.