I've had several cars shipped from California to NY. Usually costs about a grand. Last one I had shipped in 2012 was $1,100 'enclosed' which meant that the transporter had canvas sides. Better than nothing since it was during the winter but it was a little misleading.

Cost kind of depends on what level of 'care' you want. There's several outfits out there that will give your car the white glove treatment but the cost will reflect that. Most transporters take all kinds of cars. If you pick a general carrier, you're gonna have to trust that whoever loads the car on the other end can handle it.

Most of the general transport companies are brokers that work with guys they know. They're all kinda the same. Read some reviews on line.

Fuel is low right now, you could probably get it done pretty cheap if you shop around. Sometimes they give you a break if you pick it up at a hub. Also helps to be closer to a major highway.