I used freightquote for years. I designed and built custom entry doors, all were one-of-a-kind and freightquote was always reliable with a fair price.
I made the crates to handle any abuse, many were 48" wide x 10' long x 20" high and weighed 350 lbs or more. The empty crates usually weighed 150 lbs so shipping weights get heavy fast, leave plenty of room for forklift forks. And remember, the guys in the warehouse are professionals, they can put a pair of forks through anything.
The crate in the photo below weighed 575 lbs. The second crate was 360 lbs. Liftgate pickup, shipping from Tucson to Montana cost $696 in 2018, gonna be a lot more now.

The advantage of using freightquote is they are a nationwide shipping consolidator, when they talk, the trucking companies listen, truckers don't want to upset one of their biggest clients. Hiring a trucking company by yourself means they can blow you off if there is any damage or delay. If I had a problem, which was practically never, I would call my freightquote agent and he would take care of it.
Shipping rates, insurance, and class codes are tricky to figure out. Any mistake can screw you up. The cheapest shipping rate usually has the lowest included insurance, you have to read the fine print. Sometimes even the included insurance is not enough so supplemental insurance will need to be purchased. Get the class wrong and I don't know what happens but it won't be pretty.
Lift gates are extra, both at your end or at the delivery end too. Delivery to a business with a loading dock is perfect, home delivery with lift gate is the most expensive and the crate is left at the curb leaving the home owner looking at a 350 lb crate in the street. If the customer has a pickup truck the crate can be delivered to the terminal for customer pickup, that is the most affordable option. Shipments can be scheduled using the freightquote online website but I always got the best price by talking to my agent. The website is perfect for getting a freight estimate for the customer. Shipping is always extra and calculated at the end of the job. Payment in full received before shipping, that is what overnight mail and credit cards are for (add 3% for cc payments is also in the contracts).
"Freight estimate, actual amount calculated on completion" is always in my contracts. Don't forget about sales tax, most states now charge sales tax for out of state sales which wasn't always the case. Freight cost is a line item deduction on your monthly sales tax form.
The freightquote site is set up so you can download and print the BOL (Bill of Lading) and shipping labels. I printed 5 labels for every crate for the 4 sides and top, they are glued on with yellow glue and no crate was ever lost. Print 2 BOLs, truck driver signs both and one goes with the crates. I email the customer the signed BOL which has the PRO number along with photos of the crates, every step along the way is documented and everybody is happy.