In reply to ConnorMak:
Belay jacket, I'd go heavyweight if you are expecting to be standing around. Second hand is a good shout, especially if you aren't totally sure what will work for you.
Socks, I like the bridgedale summits, but it depends on you and your boots, you may be comfy in mid weight socks.
Mitts, I go as warm as you can and waterproof, they are the same as the belay jacket, you want to be warm and comfy when hanging around so you can pay attention to what's going on. Size wise, I go big so my hand can move easily, but wouldn't wear anything underneath as it insulates your fingers from warming each other.
Boots, go for the ones that fit you best, second hand can work, but make sure there is enough sole so you don't have to resole then straight away.
Water bottle, I use a 500ml peach ice tea bottle, because it has a wide neck. I prefer small bottles as you can easily keep them inside layers to prevent them freezing, fill it up on the hill too, to keep weight down. Flask wise, I don't think a small flask is worth the effort, but have a 1.2 litre Thermos (the steel one with the rattly handle, it really keeps drinks warm over 24 hrs,) that I sometimes bring so warm drinks can be better shared. I have also taken a jet boil instead of bottle and flask and just make warm juice from melted snow, which is luxury. Make your own mind up. For a course, I'd probably go for the big flask. As Tom says, make sure you are well hydrated before you leave the carpark, a 2 litre bottle of water in the car is great for this.
Emergency shelter; for who? For you, go for an orange bivvy bag, if there are more of you, get one with a size that suits. I have a 4 person one, it's robust as it sits at the bottom of a bag, doesn't get used and I want it tough enough to put up with this and not fail in high winds when I want to use it.
Buffs are good and recommended.
Don't be in too much of a rush to spend money, figure out what you want based on the experience of your first few days out. If you are in a course they should be able to provide you with all you need.