The number listed next to the challenge title is how many things you need to finish it. Listed here are all the challenges alphabetically, rather than the order they appear in the game, since they'll hop around as you complete them.
If you're going through the campaign for the first time, don't worry about going out of your way: there will be plenty of time after the credits roll and you get total freedom to finish up if you're a completionist. We'll give you some advice in completing each challenge, but you probably don't want to force it. It won't be very deep into Act 2 Missions when they'll all unlock, however. For example, the Emus Destroyed challenge is given to you by Oleg, and your character has no idea who he is prior to The Belgian Problem. Not all challenges are unlocked from the beginning. Therefore, several challenges will probably get completed just in the course of you playing the game, but there are some you may have to look out for. For example, you will be constantly gaining the Distance Traveled challenge simply by doing anything but standing still. Unlike Assassinations, Vehicle Thefts, and Activities, progress toward all challenges occurs at all times.
You earn some petty cash for doing each one, but given that there are 41 total, the total amount of profit adds up. Challenges are numerical goals of specific events in the game.
