The answer I would give is exactly what William has posted.
In short you would use high speed steel HSS, it is the best to learn with as the hardest part in learning to turn by hand is sharpening the graver. You can buy jigs for this which does make life a bit easier. Carbide gravers are for later, you will need some form of diamond lapping wheel or a diamond hone to sharpen a carbide graver. They keep their cutting edge for longer, can cut through hardened steel easily but they are quite brittle. Start with the high speed steel, size is something you will have to decide for yourself, I like to use 1.5mm square but I know others who like 2mm and 2.5mm. You can buy handles to put the graver into but I find a good size pin chuck works well for me, dont try what Bob does in his videos and use the graver without a handle, you will stab yourself in the hand and to begin with a handle makes it easier to use.
Good luck and keep us informed 
Paul.
