In the past 7 years or so I have done about 5 long distance moves. Each time I tried a different method.
I have done
1) Sell/donate absolutely everything except for two suitcases and a small box shipped. Hop on a plane.
My thoughts: very pleasant trip, but very unpleasant to have to buy so insanely much when I arrive at the new destination. Goodwill and Craigslist are great, but they don't always have what you need (especially in smaller towns where options are limited), so you will likely breakdown and buy new after a month of not having a bed/desk. In my experience it takes about a whole year to furnish an apartment buying exclusively second hand super good deals...and in my life, that's usually when I have to go.
Verdict: impractical.
2) Fill a POD, sell everything that won't fit, hop on a plane/train.
My thoughts: PODS are expensive, but the trip was pleasant, and I have most of the things I needed. The only thing I really lacked was a bed frame and I ended up just putting the mattress on the floor. Worked great. I didn't have a car at that time though.
Verdict: expensive, but it's a good solution, especially for someone living a carless lifestyle.
3) Rent a U-Haul and take absolutely everything.
My thoughts: This happened after I got a car and had been driving for a year. One thing that happens with car-owing is that you buy a lot of unnecessary but would-be-nice-to-have stuff, so my belonging multiplied. I personally really hated driving, let alone a huge truck, and it was one of the most stressful things I had to do. Loading and unloading were also excruciating. I got to my new place and realized that my new apartment was a lot smaller than the previous one, so I all of a sudden had all kinds of stuff that I don't have room for. I had to either find a bigger and more expensive place, sell the stuff, or store them in the basement of the apartment.
All of it was unpleasant, and, although renting the truck only cost half of POD, gas and insurance and motel (it was a very long drive!) combined I only saved about $150.
Verdict: expensive anyway and not fun
4) fill my car, ship the books via media mail, sell everything that won't fit, drive.
Cheapest option of all, except that I had to drive (but so much less stress compared to driving a U-Haul). I loaded up with my clothes, musical instruments, dishes, and half of my books. Sold book shelves, desk, etc. and bought them again when I got to the destination. Waiting for a good desk to show up on Craigslist was my biggest contention about this method--which is to say, not too much to complain. Having spent only on gas and media mail shipping also meant that if I want to take an extra day driving, I could afford a night in a motel. But I actually just drove to a campground and paid $20 to pitch a tent. Also, if you don't already have a place lined up, you can drive around apartment viewing with all of your belongs still in the car. Can't do that with a truck (or it'd be super expensive), and certainly can't do that if you get off the train with 5 suitcases.
verdict: ideal, especially for someone who has a car
5. ship books by media mail, take the train (you can bring two 50-lbs bags with you, and check in another three to six bags that are 50-lbs each), sell all furniture
I did this after I went back to a car-free lifestyle again. Pleasant, stress-free trip that took a really long time, but you can essentially bring as much as you would in a car. It ends up costing a little more than driving myself but it was more fun for me. The only other draw back is that you pretty much have to already have a place lined up when you arrive. So you might have to make two trips-- one to find a place to live, one to move. Otherwise it's very similar to driving your own car. The other limitation is that you can't do this moving across Canadian border. Media mail is within US only, and the train to Canada allows no checked in bags.
Verdict: almost ideal, especially for the car-less or for people who doesn't want to drive.
The next time I move I will probably do no.5 if I'm moving within US, rent a car and do no.4 if it's within the US.