I always check luggage and usually pay extra for additional bags. It’s cheaper, safer, and much faster than trying to ship items. I do know someone who shipped a whole household recently. Nowadays, you can expect to spend between $15,000 to $25,000 USD and wait about six months for it to arrive. If you have a multinational employer who will cover and manage everything, it might work, but it still won’t be quick.
Shopping locally is the way to go, anything you can buy in Argentina, especially if it’s made there, will be easier and cheaper. Even with the crazy inflation, many things are still cheaper than in the USA. Some items you’ll need to bring with you in your checked luggage. Anything imported into Argentina is usually twice the price.
Ultimately, it depends on what you consider essential. Brand-name products made in China, like Nike, JBL, and Gucci, are the hardest to find and most expensive in Argentina.