Is it OK to use the paints or paper I already have?
To get the most from the tutorials it's best to use the same equipment Anna does. The reasons she's chosen the equipment she has are covered in detail in the Equipment Page including a downloadable PDF. It is possible to substitute some paints and paper.
With paints, Anna has listed the pigment numbers on the Equipment PDF as they're the best thing to go by if you're looking to match paints between different manufacturers.
Otherwise, so long as your paints are transparent you can use your own judgement to match the paints with the ones you see Anna using in the tutorials.