I really don't have too much stuff. No furniture or car etc.

However, I have a bunch of CDs, clothes, books. It would take about half a dozen flights to take it on the plane.

So, do you reckon I should just keep taking stuff over on the plane, or is a small, cheap container a better option?

Sounds like you need to send over 1 or more pallets.

Lots of companies do this and there are a few threads on here about it I think.

Alternatively you can send over a suitcase as freight for about £90 per suitcase, door to door.