Which criticism of Darwin's theory is the best one to start with?
To my mind, the concept of a gene here or there in the DNA sequence mutating randomly and causing very small, and almost always harmful, changes in an organism seems convincing enough and well established.
But I have seen no satisfactory scientific explanation of what we see in the fossil record, which are sudden leaps by which new types of organisms appear in relatively short (from an evolutionary perspective) periods of time.
If this had occurred from the minor random genetic mutation that is well-established, it seems to me the fossil record would reveal life forms along the entire spectrum of possibilities, at every point in the spectrum. But that is not what we see, we see clumps of similar types of life forms. Furthermore, to account for the complexity of currently-existing organisms solely on the basis of random, small-scale genetic mutation, an amount of time that is for all practically purposes infinite is required, and that is not what the astrophysicists are telling us about the age of the universe.
At university I studied chemistry, with a heavy background in physics and mathematics, but did not become a professional scientist and have no particular expertise in biology, so I must limit my comments, and you can take them for what they're worth.
I will say this though; the molecular interactions among organic compounds is an immensely complex subject, and the workings of a simple cell many, many orders of magnitude of complexity beyond that, something I suggest people need to consider more fully when discussing simplistic theories of evolution to explain things.