If only this simple question had a equally simple answer. The answer is, it depends on what sort of writer you want to be.
At its simplest- you write, therefore you are a writer.
You can get away with a pen or pencil and a notebook or paper.
The costs are fairly minimal.
Perhaps you are more ambitious, you’d like to see your name in print, to be published somehow, so at a minimum you need the following.
Microsoft Word or it’s equivalent.
A computer or at least computer access. Internet connection or access to one
Depending on how you choose to submit you may need
Computer paper. Access to a printer, or your own printer.
More ambitious still? Ready to submit for publication.?
Membership of the relevant professional association for your genre of writing.
Subscription to a writing magazine. Courses to improve your skills.
Convention attendance. Business cards,
Competition entries Blog start-up and hosting costs.
Writing group membership ( if applicable) Books on writing.
The list can go on.What has been your biggest writing expense?