1. A bag. You'll need to carry your laptop and other tools to the places you want to work. For instance, I work in a coworking office. On some days, I work at a public library or a coffee shop. In all these instances, I need a good bag to carry my laptop. I'm not a stylish person, so my bag is brown and indistinct and lightweight. You could use a backpack or something with a handle.
2. Business Cards. These are a good idea. You may meet people who ask you what you do -- better if you ask them first, however. When they express interest in your work as a writer, hand them your business card. You never know. People know other people, and some of these people may one day need the services of a good writer. Marketing yourself is important, and marketing happens by building human-to-human relationships. Business cards allow people to get in touch with you. Hey, it's better than scribbling your email address on a scrap of random paper.
3. A laptop or desktop computer with an internet connection. Fairly obvious here, unless you still write with a typewriter or a pen. We live in the digital age, and that's great for writers. I remember working on a typewriter back in the early 1990s and don't wish to repeat the ordeal. You don't need an expensive device, just one with a word processor and an internet connection. I've been using a Acer Chromebook 11, for which I paid $120 at Target, for the last year, and love it. It's lightweight and basic, and I've even put stickers of flowers and fun animals on it.
4. A notebook or some paper. You may wish to take notes from time to time. Maybe you want to organize an article on paper or write a daily/weekly to-do list. Yes, you can use digital tools such as Evernote to do exactly the same things, but sometimes old-fashioned paper is the easiest way to go. I actually enjoy outlining an article on paper, executing the plan, and then rolling up the paper into a ball and tossing it into a garbage can, which signals that I can take a coffee break.
5. An office. Writers need a quiet place to work without interruption. It can be at home, but I prefer to work outside of the house, which is why I rent a coworking office space. You need a place where you can be productive, a place I'll call an office but which can be anywhere you can open your laptop. A park bench under a tree might be a good office, assuming you have a wi-fi connection.
6. Pens. See #4 above. Pen and paper work well together. I've sometimes been without a pen when I wanted to make notes. In these cases, I improvise. When at the library, I sheepishly ask the librarian for help. When at a coffee shop, I've asked baristas to lend me a pen. The point is, ask for help when you need it. Good writers can improvise and are creative. Otherwise, carry a pen with you, as I (mostly) do.
7. A smartphone. Always helpful in communicating with clients. But the apps on a smartphone are even more valuable. I record the telephone interviews I conduct with sources on an app. I organize my notes and ideas with an app. A smartphone is actually a great business tool, second only to your laptop/computer. When I'm on the bus or train, I even do research on my smartphone, then email the research to myself for later availability.
8. A website. Much like a business card, a writer needs a website to get their name out in public. If people search for you online, they should see a website marketing your skills. Prospective clients will take you more seriously if you have a website. You don't necessarily need a blog, but at least have a bio and portfolio of your best work, along with contact information. The Yellow Pages are dead -- now we have websites.
Those are my basic 8 tools for writers. Would you add or subtract any from the list, dear reader?