One factor in choosing a name is whether you intend to grow the site through word of mouth and referrals, vs. search engine optimization. If your site is viral, you want a catchy word that rolls off the tongue. The fewer syllables, the better. Some entrepeneurs like to pick a nonsense name that can grow to embody their product. On the other hand, if you expect most traffic to come from SEO, you'll want a descriptive name, to encourage users to click on your search result.
If you are on a budget, there are tools for finding what is still available. Our favorite is BustAName.com. You enter a sequence of words, and the site will show you compound-name domains that are still available.
If you are willing to spend money, many domain owners are willing to negotiate. To lower stress on yourself, you may wish to contact several owners instead of pining all your hopes on a single domain.
As is the case with most negotiations, some domain owners are interested in non-monetary as well as monetary offers. We've heard of domain owners who exchanged their domain name for introductions to influential contacts, or for famous guest speakers at their company. Be creative!