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.
Given you have a good idea of where to start and are fairly confident you are speaking the same language as your client, jump start research by generating related keyphrases and long tail variants with the ever so easy to use Google Autocomplete. This tool makes predictions based on what you are typing that are a reflection of Google search activity.
QSR (Quoted Search Results) – This is your competition. This is the number of websites using the same exact keyword you searched for.  If you aim under 400, you have a good chance of getting ranked (300 is ideal). I try and keep mine below 150 so I have a much better chance of getting results much quicker  The opportunities are truly endless for keywords and having this information is extremely helpful
Yes solid keyword data dramatically changes the game as far as rankings go. I have seen many tools that provide Cost per click stats and meaningless charts that confuse most users. the data Jaaxy provides helps drive “organic” traffic to your site on a consistent basis which will out perform PPC sites every time. I like how you say thinking like the end user, as I feel that way when I search. I dive into what people are looking for and it really helps drive content idea’s. I have seen great results from that.