I used Plycar Transportation Group when I bought my car. Shipped from Indiana to Oregon. If I remember correctly it was under $2000. Great service. You can go online and request a quote. Most shipping companies have GPS-equipped trucks so you can track your car's progress online.
You need to be careful when looking at shipping companies. Some are brokers who outsource the shipping to a variety of transporters - Montway is one of these. You want to make sure your car is with the same company throughout the duration of its journey. In some cases brokers will be cheaper, but not significantly so, and not worth the savings IMO. Shippers will quote open and closed transportation. Open is obviously just that - open, meaning your car is exposed to the elements over the course of the trip. I'd avoid that if at all possible unless you have a really tight budget. Closed can either be a hard-sided trailer or soft-sided. Either will protect your car from the elements. It will definitely need a bath once it arrives.
Also know that shippers want to run with a full trailer when ever possible. This may mean you might not have control over the specific pickup date you desire. Finally, not all shippers run East / West routes and vice versa. Some, like Intercity Lines, primarily run up and down the east coast.
Look at shippers who have experience transporting high dollar cars. Those who service RM Auctions, Barrett-Jackson and the like have the experience to handle expensive exotics. They will likely take better care of your car than your average Joe with a trailer.
Hope this helps.