Hey Tomas.
I can't suggest a company, but I can offer some advice on moving your things.
I can't say enough that you really, really, really need to cull. The rule should be that if you need and can't replace it for what it will cost to move it, bring it. Also, if it is very important to you, bring it. Otherwise, leave it there, sell it, store it.
You will have 3 entities when you move.
1. your "originator" the folks who come to your house, pack your stuff and get it to the shipping container. They usually have the contract for the whole deal and are the people you pay for the entire service. They play 2 important roles, to properly pack your belongings for their long and difficult journey and to engage reputable companies for 2 and 3.
2. Your "shipper", this is actually usually done on a space available basis and is dependent on who much stuff is moving between where you are coming from and where you are headed to. You have little to no control over this. There is insurance, it is mandatory in the states, I highly suggest it. Entire shipping containers have been lost at sea, dropped, burned and everything inside is gone. It doesn't happen often but insurance will be a godsend if you need it.
3. your "receiving agent" is the person who will go to the port here in Ba and meet your things, get them offloaded and through customs and then into a warehouse for storage or over to your new home. This is iffy stuff. These people have "relationships" with their customs officers and these relationships earn them both extra money, often at your expense. You can avoid any extra charges by:
being sure there is nothing illegal in your shipping container and ABSOLUTELY nothing brand new still in it's box. If you import new materials to Argentina in the shipping container the customs agent will assume you brought it here to sell it and will charge you outrageous import fees for it, or a large personal bribe.
be sure that ALL of your residency paperwork is in order and that you are in touch with your receiver BEFORE your things arrive at the port. Make sure he has your passport and residency information. YOU MUST BE A RESIDENT TO RECEIVE HOUSEHOLD GOODS HERE. A tourist visa does not permit this. You might be able to receive the items but it would be assumed you were going to sell them. You might be able to have them shipped to a resident who would receive them for you. This paperwork MUST be in place before your goods arrive or you will pay demurrage charges at the port which can be as much as $200 US a day depending on the mood of the customs authorities at the time.
When your good arrive there will be paperwork given to the receiver. He is required by law to provide you with these. You will need to make sure you understand the dates on the papers and what steps you need to make on an ongoing basis to be sure you are not charged by customs later for other fees. This is your responsibility. Our shipping receiver is the only Argentine who has ever cheated us - though we were warned all Argentines are dishonest in business that has not been our experience. This guy intentionally kept our paperwork, didn't tell us when important dates were coming up, waited until fees had been levied then "helped us" by getting his customs guy to accept a bribe at half the fee to let us off the hook. We finally got out from under his thumb by using an attorney to manage it. If we had gone to customs ourselves the customs officer we would have registered any complaints with was the one who was to be paid and therefor it would not have been in his best interests, or ours, to out him for his behavior.
Your shipping originator will charge you for door to door service that does not include taxes, fees, storage, demurrage, stairs or other difficult moving scenarios. If you put your things in storage, the door of the storage unit is the 2nd door. After that you are paying for another move. Moving here is not expensive, unless you use your receiver. The shipping receiver will charge you what he thinks you'll pay and he knows you don't know. Ours wanted to charge us $2000 US for a move that we contracted with local Argentine company for under $1000, including carrying the larger items up 25 flights of stairs.
My suggestion is to do business with a London based mover whose contracts and paperwork are written in your language of origin and whose laws, including insurance coverage, you are familiar with. Contracting directly with a SA company will likely not save you money on this move and it will mean you have no one to complain to who cares or understands your expectations. When you arrive you will have many opportunities to do business with Argentines.
Good luck. Feel free to write to me if you want more info or have questions.
You will need to purchase, in lieu of paying a very high import fee on your belongings, an insurance policy here, based on custom's guestimate of your things value, that ensure that the tax will be paid if you sell all of your belongings here.
It is expensive but worth it. It isn't really optional.
Peace...