I have driven a rental truck cross-country twice. This page describes a bit about how truck rental works, plus some cautionary advice.
My personal preference is to use U-Haul, so I have included their link above. I see an awful lot of Budget trucks around, so I included them too. There are a number of companies that rent trucks one-way; these are just two.
At the smaller end of the available sizes, the trucks are regular pick-ups with a truck bed rather than a regular pick-up bed. Keep that in mind when choosing a size. The smallest U-Haul truck is usually a Ford Ranger sized truck, not so good for a cross-country drive if you are a big guy like me. For my last trip, I got a truck that had an F350 base, even though I didn't even come close to using all the cargo space.
U-Haul, and probably its competitors, offers a comprehensive insurance package called something like SafeMove. It's a little bit pricey, but I usually get it just because I usually forget I'm driving a big truck. I have hit plenty of branches that just happened not to be sturdy enough to cause any damage.
Know how tall your truck is. I pay absolutely no attention to bridge heights when I'm driving my car around. You cannot afford to do the same when you're driving a truck. On interstates and US highways, there's always going to be enough clearance, but there are lots of places, namely drive-thru restaurant windows and parking garages, that a truck won't go. The embarrassment would be bad enough, but it may also be the case that your insurance won't cover cases of such blatant negligence.
A truck is not a car. This bears repeating.
A truck is not a car. A truck, especially one that is loaded with a lot of cargo, has operating characteristics that are vastly different from the automobiles to which most of us are primarily accustomed. They accelerate more slowly, they have a longer stopping distance, and they turn differently because of the additional length. Blind spots to the rear of a truck are much larger than a car's. The "sail area" of a truck causes the wind to push it around much more forcefully than it pushes a car. Exercise much caution when driving a truck.
Rental trucks do not have to stop at weigh stations as tractor trailers do. My guess is that lane restrictions that apply to trucks do not apply to rental trucks, but I have always observed them anyway.
My advice is to load your truck the day before leaving and then get a full night's sleep before leaving. The work of loading a truck, the excitement of going on a trip, and the stress of moving from one place to another can be exhausting in combination.