Is it a good move to pick 10 free blogging sites to build links
No is the simple answer really. Google is targeting these types of link building practices so I would be looking to create amazing content and the performing your outreach from there.
By Amazing content, I don't mean that you should write 500 words and how that will suffice - because for the most part, it won't. If you want to really succeed with link building, then you need to create content that takes you past what most others are doing. If you can create 10 articles in a couple of days, then you are't doing enough.
Take your time - spend a number of days creating something that is fully researched, very in depth and answers many questions. You will have a really good chance of this being picked up by a number of reputable sources.
-Andy