Be as targeted as you can as to rank high in the search result pages. The more generic the lower your ranking due to others being more targeted with their domain name, keywords and other SEO tricks. However, if you are planning on using PPC, then it is no real big deal. It's your ad placement and Ad content that people click on to go to your website.
Comment - for your Ad to be displayed in the Search Result pages, your site (site page/post) keywords must be relevant to the Ad and both the Ad and keywords must be relevant to you website title, description and content on the site.
Netherworlds you can't have a website about dogs and expect to see your ad displayed if the search keyword is "cat" and your Ad is about "birds". The keyword has to have Dog in it somewhere, the Ad has to be about Dog and on your website, the content has to be about dogs. Having the site domain about dogs and the page/post title and description have the keyword Dog in it really helps too.