It's easy and confidential using a buyer-broker to acquire a desired domain name. Our recommended domain buy service is free.
The domain name broker can also check availability of similar website names in the same or closely related categories like the web-page which led you here (which exact-match name itself may or may not be available).
If the website name which interests you is listed for-sale, the cost is based on domain-name value only, without considering value-added by existing website the domain may have.
By the way, if the domain resolves to a developed site, it's possible to include that website in the sale at a reasonable cost (if you want it vs developing or using your own site). Keep in mind the real value is typically in the domain name and rarely based on a website (except large developed sites).