The mutation is the “random” chance, the selection is hardly random. All the increasing understanding of genetics does is give us the understanding that there are many more things subject to mutation than was previously thought. It makes evolutionary adaptation more likely rather than less.
For instance, some people have larger molar teeth than other people. If we all become vegetarians eating a great deal of raw veggies, the people with larger molars will have an advantage in making use of the new diet. Evolution will select for large molars and each generation will have fewer people with small molars. So it usually isn’t some huge difference like a third arm or some such that is the subject of evolution.
Drawin’s specific conclusions don’t really hold much relevancy today. His importance in more in the direction he pointed. He made a lot of incomplete observations where he was often correct in the trend but lacking in the, as yet, undiscovered details. He didn’t have any knowledge of the function of DNA which was technically discovered in 1869 but little understood until well into the 20th Century.