We moved frequently in my years in the Navy so I've only experienced some of the "big" names who would typically win the annual contract. Most of them were okay, some breakage, damage and lost stuff each time. When we moved after I retired in 2021, we used a local moving company, to move from Metro DC to NC, suggested by our realtor. Wow we never knew how good it could be, only one item suffered slight damage which the mover pointed out to us.
We found we could save some money and POM by packing some stuff ourselves, the mover dropped off boxes, tape and paper for us to use, any leftovers they used when they came for final packout. We moved stuff like jewelry, cameras, computers, firearms, ammunition, and expensive pilferables ourselves. Interstate moves are charged by weight, not volume or number of boxes. Our mover expected a cashier's check or cash before unloading at the destination, they called us after the truck was weighed to tell us the fee so we could get to the bank before they arrived. The actual cost was pretty close to the estimate provided when they did a walkthrough. I'd also check into insurance, the moving company will have some and maybe your homeowners has some coverage, neither may be enough to cover your stuff especially if you have rare/expensive pieces.