Oh gosh, no need to use a broker. In fact, you're likely to wind up with a crappy carrier. I made the mistake of letting a corporate mover choose a carrier for my MGA once. It cost almost double what Intercity would have charged and they picked it up on a flat bed, stored it outside at a terminal, put it in a covered truck, then delivered it on a flat bed from a terminal. In at least two of those transfers (and maybe during storage) it got caught in a torrential downpour that soaked the interior. And, of course, nobody bothered to dry it out. After a two week travel time, it arrived stinking of mold and mildew.
Intercity and the other "classic" car carriers will put it in the truck at your door and deliver it to your door on the other end. Much less handling involved and much more care taken. There are others to try (no personal experience), too. Fed Ex has a division that does it, Horseless Carriage, Passport, Reliable, are all names I've seen out there. Many will allow you to get quotes online. I think you'll find the quotes will be pretty similar. Expect about $1 per mile.