From what I know your looking to gain 2 things! 1. Users linking back to your blog and 2. Sharing the content on social networks.
Building up social lists on Twitter, Facebook, Google+ etc so when you do post something new you have a hub of users to help push your post by sharing it on social networks which should also help to generate more backlinks.
Yes and there's more... Building up social lists is very challenging, it takes time and added value. The goal is to make friends with people in your or relevant to your niche. By interacting with their posts and contributing to their posts you will also be able to find good content that they are missing or add to content that they have already created. Building a social lists requires a lot of engagement, but when done properly you win.
Is this the main purpose of a blog for SEO? Would anything else apart from the above effect the SEO for the site? Maybe the freshness of content also has a positive impact!
The main purpose of your blog should be to help your users and other users that are relevant to your niche.
Also if your blog is picking up lots of links, for this example lets say 100 links a month and the rest of the site outside of the blog is picking up 10 a month will the blogs power of picking up links effect the rest of the sites rankings, would you need to anchor text link out of the posts in the blog to make the most out of it?
The blog will help the entire site.
Include anchored text where it would make sense for your users.
Example: If I had an article about creating content:
This article is about creating content bla bla and also learn how to share content bla bla bla
I would try to include my keywords, but always think of the users. Is this going to help them learn more? Is this going to entertain them?
_The external links that are generated will be natural if your content is natural. _