It's easiest to get backlinks from websites that consider your content useful and feel that linking to your site will provide value to their visitors. However, this can't be a one-way benefit; the point of seeking out a backlink is to earn additional authority, which can only come from websites that already have some authority of their own. This is why getting linked on small, new websites won't help you nearly as much as getting backlinks from an established site.
Website authority can be estimated by Domain Authority (DA) or Domain Ranking (DR), a numerical measurement of a website's predicted authority on search engines. Developed by SEO leaders Moz.com, DR can be summed up as a "score" of how valuable search engines consider that website.
Domain Ranking is on a scale of 0 - 100 with 100 as the highest score. New websites have a DR of 1 - 5, and a DR of 20 - 30 is considered good, although DR is a comparative metric, so it's normal for a site's score to fluctuate. The scale is also logarithmic, so it's much easier for a site to progress from 20 to 30 than it is to reach a higher number. Even Google itself has a DR that hovers around 95, not 100 as you might expect.
So, while DR is not a super-strict measurement of how authoritative a website is, it's an essential tool for comparing the relative authority of websites and determining great targets for your backlinks. Naturally, the higher a website's DR, the harder it will be to get their attention and prove your value so they will link to you. Targeting websites with a DR of 20 - 30 is fine, with the 31 - 50 range being the highest that are usually willing to link to sites owned by businesses with no prior relationship with them.