I've shot a few road races and triathlons for fun.
Something like a criterium or triathlon is best because they come by more than once, which means you can try different things. With a stage race, it tends to be that you are kind of just hitting the buffer on your card and hoping for the best as they come past and are gone. Also the first time I ever went to a professional cycle race, I was also quite surprised at just how quickly they do go by.
What I've learnt is that the angle you are shooting from tends to dictate what kind of shutter speed you want to go for.
If you are shooting side on as they come past you, a high shutter speed in order to keep the photo sharp tends to give a fairly boring photo, where there is no sense of motion, as the wheels and legs are completely static. It's the same as how motorsport photos look like the car is just sat still when there is no motion blur of the wheels. Instead you want to try and apply some of the same principal of motorsport shooting, where you pan and use a slower shutter speed. I've found this harder to do than motorsport, but you do get a few keepers which convey a nice sense of motion. It's very much trial and error, which again is why I'd save it for a lap race, rather than stage race.
If you are shooting with the riders more or less coming towards you, then you can use a higher shutter speed to keep it sharp without the downsides I've listed that shooting side on give you. You are best with a telephoto lens, so that you get pleasing separation and have time to get out of the way, or reach a further distance.
The most important thing though is trying to show emotion, so you really need to try and get close ups on faces, which is far better on people who aren't wearing sunglasses.