Rhys,
Are you using colour or B&W film? Do you develop your own film or send it to a lab?
The Zone System is only one approach towards getting the exposure you want. There are other ways of getting there, each with their own purpose.
There isn't really any such thing as a universally correct exposure, but there is the correct exposure for what the individual photographer wants.
One fairly standard exercise when you are starting in photography (and when you are learning a new film or even a digital camera) is to do a series of different exposures of the same scene, noting how the exposure relates to the meter reading, and what you are metering off. Then try to make the best print from each of those frames. See how the tonal relationships change, see which print you prefer, see which part of the tonal range is most important to you.
You may wish to peg your exposure to the midtones, you may wish to peg it to the highlights. You don't have to peg it to the shadows. I'd forget about trying to apply the Zone System to begin with, though there is no harm in reading and, more importantly, understanding texts about it.
Best,
Helen