From what I have investigated, you can bring the items down, and they would be duty free, but after all the fees you have to pay and problems and runarounds you will experience, I recommend that you not do this. You will end up paying thousands and thousands of dollars, if you are even able to get your stuff out of customs, it will be a miracle. I sent one big box of stuff down in 2005, and it ended up costing me around 500 dollars. I can't imagine what a half-container full of things would cost nowadays. Really, it will probably be much more economical to just buy what you need, even at the astronomical prices of Argentina. You also can only ship one appliance per shipment, so pick the washer or the dryer. Another good option is to go ahead and go to Miami, pick up the important stuff and just pay the 100 bucks for extra bags when you fly back. I know you can't do that with chairs and washers and dryers (although you could take the chairs apart and assemble them when you get in), but you can with most other household items. Believe me, trust me when I say that you do not want to ship items to Argentina. The moving company will tell you what you will pay up front, and then the customs people will add a lot of money on top of that. They will charge you whatever they want, and there's nothing you can do because they have you over a barrel.
My wife and I buy literally everything in the US and take it in bags. We have to travel anyways, and it is a pain in the butt to travel with two children and 10 different bags, but this saves thousands of dollars. We have even brought two tvs (you can carry some pretty large boxes--consult with the airlines). The nice thing is that customs agents in the airport will mostly ignore you, because they know you are a foreigner.