Actually, by far the best place to start in order to answer this question is with a Google Webmaster Tools account for your website. It's a free tool and is just as critical for running a website as Google Analytics is.
Once you have your Webmaster Tools set up, there is a section in it that will show you the keywords your site currently ranks for, and what their average ranking position is. The reason this average ranking position is so useful is that it takes into account all the search personalisation that your visitors experience. Also, this tool will tell you what keywords are already driving traffic, not just the ones you might know to ask about, as would be required with Moz or SEMRush rank-tracking tools. (And it doesn't suffer from the (not provided) issue which obscures quite a bit of the keyword info in Google Analytics.)
Does that get you started?
Paul
P.S. You can get the same info for Bing through their Bing Webmaster Tools. You should have both these Tools accounts set up right away anyway, as they are the only way the search engines can inform you if they detect problems with your site, or have imposed a manual penalty.
