Hey David,
There's no one way, we'd always recommend a healthy marketing mix - if you try multiple channels and measure them all from end to end you'll be able to assess results and see which traffic source is the best for you.
Normally, with a new site we start with a mixture of paid (paid search & paid social), as well as social community building. The reason we do this is twofold. First, social can drive good traffic that will keep coming back - so this would be from interacting with influencers and posting content on Twitter, and the same on Facebook (with a little audience growth or content reach boosting through ads). With Facebook we also recommending trying some ads that link straight to your website, as the targeting is so good and the CPC's are low to start driving some traffic.
We recommend doing a bit of paid search before you knuckle down into an organic strategy because it allows you to see how your keywords perform in terms of any conversions on site, so you can see fully where to focus. It also allows you to dictate where you want your traffic to land and for which keywords straight away, so that you can start to measure your sites performance - we wrote about it here a little more if this helps > http://datify.co.uk/role-ppc-organic-strategy/
After this it depends what's important to you - we find remarketing to people who have visited our site across the google display network to be really powerful with bringing people back, and of course organic will have a massive part to play over the longer term in driving you consistent traffic without cost attached!
In the short term too - content curation sites like inbound.org are great to post your content to.
Hope this helps give some ideas!