If I am building a new site where I want to publish my articles that have previously been published on other sites (that I do not have control over them), what is the best thing to do?
Personally, I would use canonical URLs. Example:
<link rel="canonical" href="http://othersite.com/article-name" />
Avoids any duplicate content issues and allows you to re-publish articles on your newer website. This approach is often used by blogging networks such as Gawker, etc.
Is your site going to be 100% republished content? Then I wouldn't recommend doing that.
If it is, Consider to write two extra paragraph before or after the original article (as I understand you would like to put your featured blog posts on your personal blog). This should make the content less of duplication. The authorship microdata could also help indeed.
Also, and most important, you should link from the republished post to the original post. See how Google deals with duplicate content across different blogs: http://googlewebmastercentral.blogspot.nl/2014/08/introducing-google-news-publisher-center.html
I would suggest writing the new content for new website. If the old website is not in the business / active then you can use the old content otherwise avoid using duplicate content on new website. Google will give first priority to old content not to the republished content.