SEMrush is a very useful tool for both researching competitors when starting a site or for growing an established site. I really like to find weaker niche sites that still seem to be ranking for lots of keywords; SEMrush helps me see what they are ranking for and what I can potentially target. You can also see what keywords you’re on the cusp of ranking for with your established site - another very useful feature.
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.
Jaaxy is an online keyword finder owned by Kyle Loudoun and Carson Lim that promises to help you find low-competition keywords that will help you improve your rank in the search engines. Other Jaaxy features include alphabet soup, which allows you to brainstorm for keywords; saved list, which allows you to save your list of keywords so that you can view them later; and search analysis, which lets you search what is already on search engines such as Yahoo, Google, and Bing. Jaaxy offers a free trial as you get started, and you can also choose between the pro version and the enterprise version if you like how it works.

We also have a very unique “Local Search” only keyword search that cross references the populations of all towns and cities in USA, Canada & UK. So you can put in a search like “plumber” then choose to see all the cities in “California” with a population of between 50k – 100k and it will spit out plumber suggestions attached to the locale. Pretty neat.
However, this does not mean you cannot topple them. It just takes more of an effort in terms of content as your page has to build the trust. That is why you will see the "Google dance" happening for fresh content from a site that is not yet trusted or is not very authoritative. Google gives your page a chance and measures user click-throughs when it pushes you to certain spots in the SERPs and then measures user engagement levels when the traffic hit your site through those positions in the SERPs. 
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