I am about to move from Melbourne to Bangkok and have a few tea chests of personal effects I need to send (don't care whether it's by sea or economy air). Can anyone suggest a company that provides a reliable service at a reasonable price ? 

Try Mr Google.

King & Wilson. I used them to store a mid-size containerload of goodies in Canberra for 18 mths, followed by shipment to Surin arrived 3 weeks ago - excellent condition. Good people to deal with, reasonable prices. Good Thai agent this end for getting thru Customs.

Edited June 13, 20179 yr by mfd101
typo

We've used Seven Seas multiple times without any issues and they are very good, they have an instant quote on their site.

 

What is nice is you can list an address and then prior to arrival in the port change the delivery address.

 

http://www.sevenseasworldwide.com/en-th