I just used the gumboots provided - one of the guides during the first couple of days took a list of sizes and disappeared down into one of the holds and came back with them. I was fine with what they provided, but I also wear them for work all the time and the ones they gave me were the same brand as work supplies. You will spend a fair bit of time in them, so if you have a very big or small foot or don't have luggage restrictions byo, but otherwise they will be fine. You can always wear an extra pair of socks or take the insoles out of your other shoes to make them a bit more comfy.
The jacket I took was a good (and expensive some years ago!) Goretex style coat that is wind and waterproof. I got it from one of the good outdoor stores years ago for bushwalking. I wouldn't bother with a warm ski jacket, but instead pack another layer of jumper like a thick fleece or down jacket that you wear under the coat and then can wear under the provided jacket in Antarctica.
You will be much better off with lots of layer - although it will take an age to get ready each time! I always left the boat with
- bottom half - polyprop thermals, heavy cotton pants, waterproof pants, 2 pairs of socks
- top half - polyprop long sleeve thermal, merino thermal, merino thin jacket, down jacket, provided jacket
- extremities- 2 pairs of gloves (one thin for using camera etc, a waterproof pair over top for zodiac rides), neck gaiter (tube fleece scarf thingy) and beanie.
- day pack with camera in waterproof bag and splash cover overtop
Then once walking around be prepared to take off layers and put back on if sitting around watching penguins. Always had extra jumper and spare socks in daypack for accidential gumboot flooding, but never needed them. I had lots of the gear needed in my wardrobe from years of hiking and travelling and then added little bits and pieces everytime the outdoor shops had sales, but don't go out and buy alot of gear - borrow, ebay etc if you think you wont use it again, it's sure not a fashion show.
P.S. Top tip if you want to be seen in videos and slideshows at the end wear a distinctive beanie - cos everyone is wearing matching blue jackets and covered in scarves and sunglasses!
Sorry that got a little long winded!