If by shopping, you mean Buenos Aires, there is a pedestrian street where you can purchase leather, silver and souveneirs. If you mean Antarctica, there are only two that we know of: One is Port Lockeroy and the other is a Chilean Military base. Every tour that we know of stops in Port Lockeroy, and you can purchase a variety of things particular to Antarctica as well as get your passport stamped and mail a letter postmarked Anrarctica. Unfortunately, there are big lines, so if you're not first off the ship, you'll likely wait. We assume Grand Circle is going to stop there. As far as laundry, unless you're staying in Buenos aires after your trip, you won't have time to do anything before you have to depart, and you won't need to do any laundry when you first arrive there. There are probably laundry services on the ship, which may be expensive, but under the circumstances, necessary.
As far as what to take, we're sure Grand Circle has advised you. Most tours give a fleece lined parka which will keep you warm, and which you can keep, and lend you boots, as all landings are wet ones. You will need to provide your own wateproof pants, however. We recommend some king of a head covering. We used wool caps. The parkas has a hood anyway. You can take long johns if you want, but we found it was unnecessary, as it was warmer in antarctica than in NY when we left. However, your tolerance to cold will determine that for you. The one items tha hardly anyone considers is gloves. You will need rubberized gloves, because the biggestg problem you will have in Antarctica is staying dry. Visit a local tackle shop and purchase a pair of rubberized gloves with a pair of liners, with a split forefinger, the kind surfcasters use. This will permit you to take pictures by exposing only the finger which will snap the shutter while keeping the rest of your hands warm and dry. We were the only ones who had those gloves, and the only ones whose hands didn't get frostbitten.