Are you planning on stopping every night or switching drivers? We've done it both ways driving across the country and sometimes we just want to get there and drive straight through.
Vegetables and non-greasy foods are your friend, and we'd seldom stop for a large meal as it just weighs you down and sits heavy. Snacks are good to keep you going.
Don't let your fuel get below 1/4 tank. Fuel stations can be far apart and we've come across them only to find them closed.
Waze is a great app for notifying you of where police are located on the roadways and to route you around traffic.
Plan ahead if there are any stops or sights you want to see along the way.
We prefer books on tape since you can get lost in the book and the time seems to pass better.
Soft ear plugs are great for when you want to catch some sleep.
Know your route and look at construction/cities so you can minimize downtime in traffic. This time of year you might want to consider a southern truckers route to stay away from the mountains. Western mountains sometimes require chains to cross them.
Pump up your tires to accommodate the additional load of the car and reduce rolling resistance, just don't go too high.
Change the oil in the car and service it since it's a long drive. Make sure it's up to snuff. A simple ball joint or wheel bearing failure could delay your trip several days waiting for parts.
Set up emergency points in case you run into trouble. For instance, I can assist if you're in the Arizona area. While I may not know your car, at least it's a friendly place from which to make arrangements instead of some random parking lot.
Make sure the passengers seat reclines for napping. Don't stuff the car so full you can't move.
We prefer not to make plans when driving across country as those plans will always change. It was easy to find hotels along the route at the last minute, even pet friendly ones that weren't expensive.
Have a credit card or other means of emergency money available that is only for use in an emergency. We needed to rush home for an emergency when in Italy and it cost us $4,000 to exit the country in 24 hours.
If you're towing or have stuff strapped to the car, make sure it's bombproof. On our first drive from Maine to Arizona, the Thule roof racks tore off the top of the car and sent $12,000 worth of bikes bouncing down the middle of the highway. I was able to get them before they were destroyed, but then had to make alternate means of securing them, which I did because I was prepared. The damage to the car was over $8k but luckily the bikes were OK (the titanium one took the main hit, saving the carbon fiber from certain destruction).
Check your bank accounts before leaving. On one of our drives from Maine to Florida, while on the drive I checked my account and noticed a simple $2 charge from a place in NH to which I'd never been. Turns out it was a scammer pinging my account to see if money could be withdrawn. They ping the account for a small amount and then when nothing is done, hit it hard. My bank was able to turn off the card for remote purchases, so I had to use my PIN or be present for the card to work, but it was less than ideal for the following 2 weeks.
I think that's it.