As Nicolas rightly says, LinkedIn is where your clients are likely to be found – not Facebook or Twitter.

That said, I wouldn't pay to use LinkedIn ads in this case. Not initially. Your target niche is quite narrow, and LinkedIn's targeting might be far too broad. Compare your own ability to home in on likely clients using LinkedIn to the shotgun approach of LinkedIn ads. And also consider whether someone is more likely to respond to a hand-crafted message or an ad. Before you pay for LinkedIn ads, test your own ability to get leads from LinkedIn through your own manual efforts. If you cannot, then LinkedIn ads cannot. If you can, then you may still be more efficient than LinkedIn ads.

Apart from that, the main strategy I'd pursue (in your shoes) would be SEM. That might mean PPC ads in Google and Bing. It should also include some intelligent SEO copywriting to ensure that you're indexed and can be found organically. That's something you – as a writer – can figure out and accomplish on your own.

If you'd like advice on branding, naming, and domain selection, then talk to me.