The Google Keyword Tool is SUPER helpful for building a foundation for your keyword research strategy. At the end of the day, these search numbers are coming straight from the horses mouth. You can filter down to a hyper-local level and see which keywords are getting the largest search volume. Plus, with it’s integration with PPC you can get a quick idea about commercial intent by looking at the bid and competition metrics. How much are people bidding on KWs, higher = more likely to generate a return. Usually its aligned with search intent. That said, the trending data is a little less reliable. I would still use Trends to analyze the popularity/ seasonality of KW search volume.
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.