I did the CELTA recently, and this is a list of what I eventually had to buy:
1. A huge folder to keep all the handouts. Best to get something that will allow you to flip through the notes easily: you will be doing a lot of flipping!
2. Notebook & all kinds of stationery (pens, stapler, hole-punch, highlighters, etc) -- things that you would use as a student!
3. A folder to keep your most current lesson plan, which you have to hand to your tutor before you teach a lesson.
Best check with the centre that you've registered with for a list of other things they expect you to bring. I didn't have to bring stuff like paper & whiteboard markers because all those things were provided.