1) SEMrush - I believe that among all the 3rd party software, SEMrush has the largest keyword database. Their search volume data is pretty accurate and aligns with the Google keyword planner. Also, based on the type of content that needs to be produced (i.e. informational, transactional, etc.), one can utilize different filtering options available in it.
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.