Sometime back, I saw a website offering 'hosting for work at home moms' and this seemed to be a very different idea as typically hosting companies target a broad range of customers. As you might imagine, work at home mom and dads would be an ideal customer for wanting hosting as many don't have previous webmaster experience. You would want to familiarize yourself with the needs of this niche before trying it out.
Yes, you can definitely focus on a niche, I believe that may be the best way to really be able to cut into this industry as there are so many in it. A niche will put you above your competition within that section.
It can be anywhere between, web hosting for gaming clans, to web hosting for bloggers.