Yeah like they said, the biggest issue will be the import duties on stuff shipped to you.
I have a friend who tells me that when he goes to the airport to get something shipped to him, that he never pays import duties because he has no DNI. According to him, if you act like you don't understand what you have to pay for, tell them you don't have a DNI, they won't charge you import duties. Really, I don't believe this, but he insists. I still don't believe. Heh. Who knows?
The other thing is that you may have trouble getting an online purchase shipped directly to you. I have heard that Amazon, for example, used to ship to Argentina directly, but no longer will.
I have a mail forwarding service in the US from a place called USABox.com. Get this setup before you leave anyway - it costs me $29 a month. I have all my mail from the States forwarded there. That price includes storing your mail, displaying photos of it online and a free shipment from DHL once a month up to a certain weight/size. You can choose what to send and what to throw away (in the case of junk mail - and you can throw junk away anytime). I can also send as many times as I want during the month, but at an additional, low cost after the first free one. Much lower than if I were to use DHL myself, for example.
I usually receive things shipped from USABox within 2-3 days. I've only had problems once, when because of my address (no street number or anything, basically just directions) a package got sent to Mar del Plata, but I tracked it via DHL, saw where it went, got it straightened out in short order.
So you could have things sent from sites that won't ship to Argentina to your USABox and forward it from there to here. Depending on what it is (size and weight) you may have to pay a bit more for the shipment. Also depending on what it is, USABox will repack it if it will save money with DHL as far as the size goes. They will create the invoice and all for customs.
As far as what to bring - bring your favorite deoderants. I don't like the deoderant here. Bring some spices that are not salt, pepper and all the "regular" spices like paprika or ground red pepper because you can find that sort of stuff. For example, if you use Old Bay, bring that. Steak seasonings that you like, etc. Garlic salt I have found down here once, but you could make that if you had to.
Electronics you know.
The rest of it - you are going to live down here, may as well get used to it and figure out how to find what else you need and live without that you can't find.