Chapters 1 through 5 are essentially an extended training session, and it could easily be argued that 6 is included in there, but I've always considered that more of an interlude. These ones take place during the winter (why I always associate this game with Christmas lol) 1945
Chapter 1 is pure tutorial, you learn how to acquire and utilize munitions and some basic character control. This mission is essentially impossible to screw up and can even be skipped with nothing lost, but I've always like it for the color it adds to Vito. This area cannot be revisited, but there is no reason to go back anyway, there are no collectibles present.
Chapter 2 is where you learn to drive, refine the basic mechanics of shooting and movement, and learn to fight. One thing to note, early in the mission while walking to Joe's apartment you overhear a conversation centered on a broken down car; this is easy to miss/skip, but its actually designed to teach you how to fix cars, which are prone to breaking down when you are learning to drive. Joe will teach you how to both drive and steal cars, alongside a nice little lock picking tutorial, and give you experience on evading the police, which also teaches you about body shops where cars can be upgraded. This one wraps up with your first solo mission which allows you to put all your new found skills to the test in a neat package. Big thing I missed my first time playing the game, you just learned how to make money; steal cars and bring them to the junkyard, every time you put one in the crusher you get 500.00
Chapter 3 introduces you to several new and important characters and give you a chance to refine many of the skills you have picked up. After the dock sequence you will be given a job to do solo, it specifies nobody dies, but what it actually means is no one gets shot, you can stealth kill everyone, although I enjoy doing this one without killing anyone. Two things to note here:
Its not exactly obvious, but before opening the safe go into the basement and disable the alarm. Its apparent if you're paying attention, but no one goes out of their way to show you this.
Make sure you've got a decent car for this mission. In the later editions you are given a couple of jeeps, one is army issue, the other is a civilian model of the same thing, I like to use the civilian one for this becuase the final stages take place late at night and the roads are very slippery, the extra traction far outweighs the speed of the fancier cars. Whichever car you use hit the body shop to upgrade it as much as possible, the time line can get tight.
Chapter 4 adds almost nothing new expect for a location that can never be visited again (like many in this game). Make sure you are watching for magazines as this is your only chance to collect some of them. After the job is done you will be left to get home alone while the police are actively searching for you, and with the number of cops you shot they want you badly; you will need to steal a car and it is advised to stop by a clothing store to get a change, with a new suit you will be unrecognizable.
Chapter 5 introduces you to Harry, you very much want to know Harry! Guns can be bought at most street corners, but those are the pea shooters. In time Harry will carry automatic weapons, rifles, grenades, and, my favorite, the 357 magnum (its like a tiny sniper rifle in your pocket). After a short refresher on how to fight (foreshadowing the next chapter) you will be tasked to go meet Harry for some firepower and meet up with Joe and Henry (your new best friend). This is pretty much a final exam for the tutorial setup, big shootouts and car chases ensue, if you got this far you should have no problem, so just enjoy the story as it unfold.