Welcome to guru. I will start by saying that I only PvE.
1. Each chapter - Prophecies, Factions, Nightfall - is a standalone game that can be linked to another by adding the key to your existing account.
2. As stated, the sticky at the top of the Q&A forum (Player on a budget) explains the differences between each chapter.
3. Prophecies is overall the favorite for beginners. Requires the least knowledge of the game. You get to learn as you go. Also has the greatest scenery.
4.Nightfall is favored when you want to start off with customizable heroes (henchmen), but this does require knowledge of builds for other professions to make them useful. Otherwise you are better off with the henchmen.
5. Very sweet chapter, I loved it. But it was my second purchase, and the quick trip through training to level 20 monsters on the mainland was not as traumatic as if it was my first experience.
6. All game features, excepting chapter-specific professions/skills and NF heroes, are universal, or even if started in one chapter, soon become universal. ArenaNet has constantly updated the servers throughout the life of the Guild Wars world. Ask any player/forum member who has owned the game since it went retail two years ago, and they will tell you it is not the same game.
You can also check for more info on
http://gw.gamewikis.org/wiki/Main_Page
Enjoy the game, whichever you buy.