Long-distance cycling under AUK rules is often (though inaccurately) referred to as audaxing. Mudguards are not required for any of these events. Use whatever bike suits you. If you don't want to follow a routesheet then download the GPS file, but do ensure you read the information on the routesheet as well as in the event webpage. You will need to be fit and self-sufficient. Most of these events, especially the longer ones, are hard. You should be an experienced cyclist with both fitness and stamina. There is a minimum speed of 15kph for all the events of 200km and above. Don't worry about the maximum speed of 30kph, you won't get near it. Prepare your bike and yourself carefully for any of these events. If you do all the distances, you become an Exeter Wheelers Super Randonneur.
More complete advice and other infomation is at Audax UK.