It's good to decide early on if you want to have a brand domain or a keyword domain. The benefit of a brand domain is that your domain will most likely be considered as trustworthy, and immediately shows visitors that it's linked to your business or personal blog. A keyword domain, on the other hand, has the advantage that it will be better optimized for search engines, and therefore will get higher search results. In recent years, however, the drastic improvement in search results thanks to a keyword domain has begun to decrease.
A short, one-word name (ex. cat.com), and especially .com domains, will be pricy because simple titles have a lot of potential uses, meaning people probably already check them out on their own. If you are going after a registered .com domain, you will have to contact the current owner, and even then, prices could be high for misspellings and multiple word domains. In the past years, companies and individuals have settled for bizarre names, misspellings, and old tricks like adding “the” or “my” to the front; note, however, that this will also reduce domain performance.
^ Mockapetris, P.V. (November 1987). "Domain names - concepts and facilities" (HTML). IETF Documents. IETF. doi:10.17487/RFC1034. Retrieved 24 July 2017. Relative names are either taken relative to a well known origin, or to a list of domains used as a search list. Relative names appear mostly at the user interface, where their interpretation varies from implementation to implementation, and in master files, where they are relative to a single origin domain name. The most common interpretation uses the root "." as either the single origin or as one of the members of the search list, so a multi-label relative name is often one where the trailing dot has been omitted to save typing.
Even if the term isn’t trademarked, don’t buy domains that are just a variation of another domain name. This means avoiding plurals if the singular is taken (mediatemple.net vs. mediatemples.net), hyphenating a phrase (media-temple.net), or adding “my” or some other preposition (mymediatemple.net). Alternately, you might consider buying these variations yourself and set them up so that if someone types one of the variations, they are redirected to your main site.