Facebook is terrific, but I use it for personal matters, and don't like to mix it with business. For professional matters, Linked In is okay, but its interface is not nearly as "rich" or engaging as Facebook.
Go for easier keywords untill your site builds up enough strength for those hard to get keywords, although a couple of strong links using the keywords you want as anchor text might get it onto page one.
Quantity only becomes important in the context of quality. You might have hundreds of low quality links pointing to a page, but I can probably outrank that page with a handful of high quality links pointing to my page.Now if we both have similar quality links then whoever has more is probably in bet...
There are lots of SEO techniques that can help your website to come up on a search engine. Article submission, link submission etc are the effective techniques. Update your website content regularly, this will also help your website to come up.