I shipped a 67 from Kansas to the UK. I went with a middleman that arranged everything for me, so there was no hassle on my behalf. The sea-freight company they used was Schumacher Cargo. If I were to do this again, I'd definitely use a freight company directly, as most will offer a door-to-door service, and as no registration paperwork was needed in my case (car undriveable) the middleman I used was probably not the most efficient way of going about it.

If the car doesn't run it's no problem, the transport people will be able to load it. It means that you'll have to use a container though, not a RORO (roll-on-roll-off) ferry.

You would need the original certificate of title to be able to export and import.

You do have the option of air freight, but from the quotes I got, that's about twice the price of by sea - a lot quicker if you can afford it though.

The company Wouter recommended is a lot (LOT!) cheaper than what I paid, and a greater distance to travel than mine, so I'd look at them first.

For parts I've used 2 catalog companies, Classic Industries and National Parts Depot. I can't compare the quality of parts from each company but I'm pleased with everything I have received. NPD was by far the quickest to respond to emails (matter of hours, compared to days with Classic)...both offer international air-shipping. If the parts are with the car already you can just ship them with the car in the same container.