I love this: "You will understand certain concepts to the bone and not just learn their meaning from secondary sources." I've so often wished I could read great works of literature in the languages they were written in so I could get the real flavor. But I never thought about learning a dead language so I could understand English better. Here I always thought Latin was just something used to torture schoolchildren in years gone by...
Learning any language will help you to understand your own better. One of the advantages to learning Latin is that so much English vocabulary is borrowed from Latin directly, or indirectly via French. This also makes learning Latin easier, since you already know a lot of the words.
Lingua latina is an amazing language to learn. I recommend https://www.youtube.com/user/latintutorial to start with.