Where do you live? Most people who inquire about expediting on this forum do not indicate where they live. The answers you may receive can be very different depending on where you live, how often you want to get back home, etc. Expediting from a home base of Detroit, Chicago, Dayton, Buffalo, etc. would be quite different than if your home base is New York, Jacsonville, etc.
If you don't care how often you get home, perhaps it doesn't matter where you live--but most people like to get home regularly. Being based in Detroit, I got home often, even if it would be only a few hours sometimes. Also, I could be 12th on the board on Monday morning, and still be out by early afternoon.
While I did not like the rates and the high percentage of GM loads at Tristate (Perrysburg, OH), I thought their dispatch system was the fairest and provided the best training for a newbie. If you decide to be a single driver, and if you live in MI, OH, IL, IN Tristate would provide the most steady miles. They have no experience requirement.
Landstar is a good one for team drivers. They require six-months experience. Their dispatch system using various agents, compared with central dispatch which the others use, takes a while to get accustomed to.