Don’t rush this, what phrases or names relate to your niche?
Do you want to build your own brand? Is your name taken? If you are wanted to publish anonymously you can create a pseudonym and see if that is available. Check to see what is already out there that is similar to the name you are thinking of as there maybe complications down the line.
There are a number of different names extensions available but rather than limit your market reach with some people not trusting the latest gTLDs which are domain extensions such as .ninja,.guru or.legal. The majority of people will trust a .co.uk or .com extension.
You can check your domain at a number of different domain hosting sites however hang fire as depending on the next step and what web hosting you use you can save yourself a big headache as they will integrate it for you rather then you having to modify DNS servers and redirect your domain.
Before you commit to the domain name check what Facebook pages or twitter accounts use the domain name already as their brand identity, you want to be able to create as many places to redirect by to your site as possible. It could be that you can just slightly change a Facebook page or twitter name to work with your domain for it still make sense to the person looking at your brand network.