Such a big topic, how to move the car from one place to the next, lots of options. I am going to outline my plan for exploring the various options: buy a truck (what kind of truck, what is the best tow vehicle) and trailer (what kind of trailer open/closed, steel/aluminum), use some type of service like a car hauler, or through an arrive and drive program.
Almost all of the research that I have done on tow vehicles point to a diesel Hemi as the way to go for a reliable solution to towing pretty much anything. This is where personal preference, budget, and other factors come into play. Right now I do not have a car capable of the towing capacity needed for my car, or possible future trailer. My budget will not allow for a dedicated towing vehicle so if I decide to go down this route, I will need something that can serve as a daily driver as well. Which is steering me more toward a gas, rather than diesel truck, or possibly an SUV. For options around trailers, an open steel trailer is the most economical but will weigh more, and may play a factor in tow vehicle selection, a open aluminum trailer is the next best option as it is lighter and would not require as much towing capacity. Depending on space and storage options, an enclosed trailer seems to be the best options but, storage (where to park it when not used), weight, and cost become the primary factors. The above are examples of what I found on racingjunk.com
The next option would be to find a dedicated car hauling service, the above is one provider unitedroutes.com you would contract with them directly, and are typically charged for a per mile fee. I have been quoted anywhere between $1.50/mile to $0.80/mile, there is generally a nominal load/unload fee as well. I have not explored this option too deeply but may look into it further as things progress.
The current solution I am exploring will be an arrive, and drive it includes the per mile fee, and the load/unload fee but is also bundled with a crew per day cost. I am going to try this out next weekend with Winding Road for a trip down to Houston for an LSR DE. As I am not fully committed with a full blown race car, this allows me to explore multiple options, before committing to purchasing a car transportation solution.