Its important that you setup your social channels and interlink them and then engage with your users on social with the right content and drive traffic to your site through these channels. Racking up fake signals and fake followers who do not engage or visit your site through the channels, is easily detected by Google as false and it does not help your rankings.
Of all the tools listed in this article, Moz Link explorer is an old one & quite popular. If you want to compare backlinks between two or more domains, Open Site Explorer is worth trying. This tool works best when you have a paid account of SEOMOZ though a free version of this tool is good enough to get you started checking the backlinks of your site and the sites of your competitors.