One of the primary things you should be striving towards with your brand website is status as an authority site. Simply put, an authority website is one that users trust as well as industry experts and search engines.
The sites that have achieved this level of trust are often major news publishers. Though a large proportion are news providers, it is not a rule, many are highly regarded blogs with a clear niche audience.
Unsurprisingly, it is Google that decides which sites qualify as an authority website and which do not. If Google considers your website to be trustworthy, this has the potential to greatly influence users. Google is a link that is worth having; one major link will be more beneficial that several links from smaller sites.
To form these links, you should build your audience first. It is an audience that will attract the links to your website. One of the best ways to build your audience is to post regular high-quality content that is accessible across all formats.
When you’re posting content, you should consider whether what you’re posting is interesting to your audience and whether it is evergreen; meaning that it will be relevant for a long time.
To check your site, or someone else's for that matter, use Moz. Moz has a site explorer that will rank the site out of 100 based on its authority. Do remember, however, that this is a score from Moz, not necessarily Google, so treat this like an educated guess.