When moving your worldly possessions it is advisable to use a company that has been recommended by someone and that there reputation precedes them.
There are companies that are affiliated to organisations such as the International federation of Removers FIDI or Overseas Moving International OMNI.
It is worth noting that small unregistered companies have been known to disappear with their clients belongings although on the other hand small companies can be extremely reliable.
You should get at least 3 written quotes as rates can vary considerably, the company should send someone along to give you a detailed written quotation and should if required pack your belongings for you.
Make sure you are insured, you should expect to pay anything from 3000-6000 euros to move the contents of a three bedroomed house within western Europe for example from the Midlands to the middle of Spain. If you are flexible about delivery time you could share the delivery with someone else hence reducing the costs for the both of you!
You could also (for insurance purposes) take photos of valuables of which the premiums are usually 1-2% of the declared value of the goods.
You also need to take storage into consideration because if you do not need or want your belongings straight away this can sometimes be included in the price but is sometimes added on per period of storage.
Make sure you have vehicular access at both ends of the trip especially if you are moving to a remote area where roads and openings can be quite tricky for a large heavy vehicle