If I may, I'd like to buck the trend here a bit. We do not really know what the OP wants out of the equipment. If one were to want discrete shooting in the street and interiors, then a 24-70 would be a rather poor selection. For convenience and overall sharpness, then the zoom will come out on top but if the OP wants to frame something that the 100mm does well, then the 24-70 will have to be shot wide and then cropped in post. If shooting film, this may be more hassle than it is worth.
There are just so many possible photographic situations with ideal equipment selections for each that it is truly impossible to suggest an ideal without knowing the use scenario.
That said, why not get the 50, 100, and the zoom? 50 is inexpensive and a low light monster, the 100 covers a focal length the zoom does not cover, and the zoom can be used when the focal range is right and IQ is paramount.
I agree with this - the choice is not so clear cut and I am surprised by the consensus.
The combination of primes suggested by the OP is about 5-600 USD less than the zoom with the major online US retailers (OP's local prices might differ of course). Closer in price would be : Sigma 35mm f/1.4 + Canon 85mm f/1.8 + Canon 135 mm f/2 L. This gives an even wider range of focal lengths and includes two lenses in the 35/135 combination that are widely considered to be exceptionally good.
I'm not necessarily advocating this particular combination of primes - maybe OP would prefer something wider - just pointing out that there are other options and the situation is not black and white. Yet another similarly priced option would be the 35/85 combination above, plus the 24-105 f/4 L.
My own suggestion to the OP would be not to buy anything at the moment, and look to borrow and/or rent some of these options to figure out what is really needed.