Forget expediting at this time. Not to sound harsh, but here's the short version of things. You need to spend a few dozen hours reading these forums to learn what "typical" expediting is all about. I will soon be criticized and told there's nothing typical about expediting and to some extent that's true. One fairly typical thing is expediting is driving from point A to point B to C, D, E, F, G, C, H, I, J, K, L, B, M, N, O, P, C, Q..... with a few times being to the same customer and most being unique each time. If you lived around OH or other central location you might get near enough home to go home every 2 or 3 weekends. From Tampa you'll be way too far from home to deadhead home.
As to who pays and how you are paid, that's partly covered frequently in here (who pays what) and how you are paid is based on how the owner does things.
Again, I'm not trying to pick on you personally, but you need to have a stronger foundation in expediting in general to understand what this field is all about and to know all the questions to ask before accepting any position. Most importantly, be sure you have a written agreement if/when you finally do anything.
Good luck to you but I don't think this career is right for you at this time given your need to be home.