Keyword searching is one of the most important part of SEO(Search Engine Optimization). It is the way to promote(attract the visitor) any website or specific articles. When a website made basis on the different(keyword) for those articles. There are many tools for searching and sorting the appropriate keyword. Google Analytic s and Adwords are best of all.
Yep keyword research is very important. Although nowadays we don't need to stress over it like in the past. You don't need to mention your keywords as much in your content, but it can still bring you long term, free traffic to your site so sholdn't be overlooked.
And Google Adwords keyword tool would be good for keyword research I would say, as it is based on mainly Google data.
Instead of considering Google page rank if we put more work and importance for SEPRs for particular keyword means then its more useful for our site.