Charle, about tools, instead of buying them straight ahead, rent some equipment if possible, especially if it´s for a course, so that you can see which crampons you feel better with, which height is best for the ice axes etc. Especially considering you´re taking two courses and then Aconcagua which is not technical. It´s besto to rent/borrow and try some options before chosing something for yourself.
By the time you go the Alps, if you really enjoyed climbing (which you probably will) you may buy stuff there, and you can do so in Chamonix, but at least you´ll know what you need and how to buy, plus, there´s the weight issue on airplanes.
Regarding clothes, do invest in good gloves and socks. I highly recommend Black Diamond Front Pointer GTX gaiters, absolutely crampon proof. For sunglasses, go ahead and buy a category 4 already.