Cadmium red is certainly truer than crimson or rose, but it is slightly towards the orange side of the color wheel so it's not a "true red" but I am not familiar with any "true" reds in watercolor, but it doesn't mean you can't mix colors as though cad red is true red, you just want to be aware there is some slight yellow in the pigment before you start mixing.
This pdf is really helpful for color choice and mixing. http://www.wetcanvas.com/Dan/wca_color_mingling.pdf
Also, I have a sheet of paper that I have drawn a circle on, and then every time I get a new watercolor, I put a dot of it on the color wheel (with the name written next to it) where I see it fitting in best (test on a scratch paper first, to see it's color). This way, you can see at a glance what red that you have is closest to "true" red and how colors all align to each other. Good luck!