What exactly am I supposed to know when progressing through Personal Story?

You should be able to play and enjoy most of the game without much prior background information - as long as you're aware that you are taking part in a world with a rich history and don't mind not getting a few references. This is probably how the majority of players proceed through the game.

For those who do want to get all the references and understand the lore of Tyria as completely as possible, you would have to go along the following steps and pay attention in cut scenes and dialogues (or at least substitute reading up on them in the wiki, which does a fairly good job of summarising them):

• Play through the original Guild Wars game
  • Prophecies
  • Factions
  • Nightfall
  • Eye of the North
  • Guild Wars Beyond storylines
• Read the novels bridging the original game and Guild Wars 2
  • Ghosts of Ascalon
  • Edge of Destiny (this one includes what happened with Glint and Snaff)
  • Sea of Sorrows
• Go through the storylines and dungeons as they become available when you level up (the third dungeon step below intertwines with the first two):
  • Play through the initial storylines of each of GW2's 5 races (Parts I through III) and through the Orders storyline (Parts IV through VI) with at least one of the orders
  • Play through the Pact storyline (Parts VII and VIII) with at least one character
  • Play through the story mode of each dungeon as part of the storyline (you'll get an in-game mail from your "herald" when you've reached the appropriate level, though it may be easier to go through dungeons later. So Ascalonian Catacombs, if I remember correctly, would be after Part III of the storyline where you'd be level 30, and so on. Skipping these dungeon stories may mean you don't get some references in the story that takes place "afterwards". Explorable modes of dungeons are, shall we say, bonus material and not strictly necessary to understand the storyline.
• Play through the first parts of the Living World story (though some of this is not replayable, so if you missed out of it at the time, you'll have to read up on it - or watch YouTube videos of it if available)
  • Living World season 1 - Scarlet's War, although I believe not all of this is relevant to the larger storyline, e.g. Shadow of the Mad King is only relevant to the Halloween events, and The Lost Shores mainly introduced Southsun and the karka (but also characters like Canach if you're interested in his backstory)
  • Living World season 2 - these can be replayed at any time, provided you logged in at the right time or unlock them later via the Gem Store
• Play through the storyline of the Heart of Thorns expansion
• Play through the rest of the Living World
  • So far, there's Living World Season 3
  • (future content...)

I guess the game developers wanted to strike a balance between offering GW aficionados a rich history of the world in which to play while allowing newcomers enough context to get going without forcing lore down their throat, and without forcing you to do everything in the "right" order. I understand how someone not familiar with the backstory might find some references confusing if they're the sort of person who wants to understand it all (as I suppose the OP does), but personally, I think they did a pretty good job of striking that balance.

How much of all this (which would take quite a large amount of time) one wants to do and how much one wants to skip is up to each player, of course.

Converted my long comment into an answer.

Most of the points raised are addressed in the Guild Wars story, if you've not played the previous game, I can understand why some of this might seem confusing.

You can catch up on the Guild Wars wiki, if you're interested, https://wiki.guildwars.com/wiki/Storyline.

The previous game happened 250 years prior to Guild Wars 2, hence why some of the story may appear to be glossed over. This is probably to give some narrative flexibility because of the large in-game timeframe.

To sum up, no, you've not done anything out or order at all. You're just playing a sequel to a game in which the world still exists directly from the events in the first game.

The story is only developed in story instances. So unless you've started the story of Scarlet's War (Living Season 1), Living Season 2, Heart of Thorns or Living Season 3, or unless you haven't spoiled yourself on the wiki, you haven't had any information you shouldn't have.

There will be more about Glint, just not yet if you follow the intended order of the story (which I conveniently listed in order).