i recently drove about 500 miles with my cat
i used the Dura-Ruff folding carrier. it is nice because it opens from the front and the top, plus you can roll open the sides as well so they can see what is going on. I used small box and lined it with a bag and put litter in it, i put that in the carrier for my cat. the Dura-Ruff is big enough for at least two or three small cats, one really big one. but for the long ride, my cat didnt stay in for very long. only on the very curvy parts of the road. he wanted to explore the rest of the car, or sit on the carrier and look out the window. also, the great thing about the Dura-Ruff, is it folds nearly flat when you are done using it!
about a month before the departure i opened up the carrier and left it completely open, so he could wander in and out, and it wouldnt be a brand new thing. i recommend this with any carrier. also, put a favorite pillow or blanket they have in there. any favorite toys. seeing familiar things makes them feel better.
remember that while cats are independent they also like their routines and the familiar. so there probably wont be a way to drive them all that way with them perfectly O.K., but there are ways to make them as LEAST anxious as possible.
NOTE: when letting a cat out in the car; make sure there is someone in the front seat with you to make sure the cat(s) dont go for the pedals. EXTREMELY important. cats under brake petals = BAD
Same rules apply for planes. a 3000 mile plane ride is still a good 6 hours on the plane, plus travel time to the airport, and from the airport estimating another 2 hours and going through security est 30 min. a cat who is not used to travel will get very anxious being in a carrier being carried one place to another for 8 1/2 hours. plus cabin pressure is worse for animals than it is for people. if you have to do it, do it, but if there is another way. i would recommend drive. even if it takes longer.