Pen and paper works fine...primarily need it just to give you a good idea of what your end product will look like because while you're putting it from mind to paper there is a lot that will usually change and there's a lot you'll realize you'll need to consider once you're actually thinking about everything in enough detail to be able to write it down.
But yeah, pen(or pencil) and paper will be just fine. I'll usually start by writing lightly so when I make mistakes I can just write over it normally and when I make mistakes with that I can go over it a few times to make the lines darker....then after I'll take what I have and redo it real quick on a fresh piece of paper so I have a nice clean copy with no cross outs or write overs.
But yeah, pen(or pencil) and paper will be just fine. I'll usually start by writing lightly so when I make mistakes I can just write over it normally and when I make mistakes with that I can go over it a few times to make the lines darker....then after I'll take what I have and redo it real quick on a fresh piece of paper so I have a nice clean copy with no cross outs or write overs.