Remember, depending on the route you take, there are areas where there will be no cell phone service.
Even if traveling in summer, take a jacket or sweatshirt, and a few heavy clothes, because it can snow any month and be cold in areas of the country.
Watch the weather carefully and be prepared to alter your route if necessary. At this time, there is a storm hitting south Florida that is expected to cross into the Gulf and hit the Gulf coast states by mid-week. Lots of rain and flash flooding expected. Make sure you have a good weather radio with alerts with you. When traveling through areas like Tornado Alley, when you stop for the night make sure you know where the storm shelters are located.
If traveling more than 3000 miles +/-, consider planning an oil service stop somewhere along your route, and if on a schedule, make a reservation for the service.
Make sure your medical coverage is good where you plan to travel.
Plan for rainy days, take your rain gear. But also have some things to do inside the rig in case you find yourself in torrential downpours.
Have fun and safe travels.