In Situ Introductions
Also sometimes called 'in medias res', this assume that the group is already a group. You should sit down with your players, and get them to make up what kind of group they are (mercenary company, treasure hunters, powerful Knights of the Kingdom, a group of childhood friends who all pledged to become adventurers, the graduating class of a martial academie, one guy who has worked with all these other guys before, etc), and alter your beginning plot hooks to be specific to the kind of group. They should work out if the group has a name, what it is, and how they present themselves to the rest of the group 'the grim guy', 'the funny guy', 'the practical guy', 'the head-in-the-clouds wizard' etc. This is a character-building exercise. It's also a great excuse for why they're working together.
Sometimes you know a guy, and that guy knows another guy, and that guy has worked with another guy, and that guy has a clingy girlfriend who refuses to be left behind and is really, really good with knives. This style of storyline starts with one character getting given a story hook, which he knows he'll need some help to roll up. Then, going around the table, the characters daisy-chain how they know the previous guy (or a different guy already in the group) and why they'd be willing to come along. It neatly puts motivation in the hands of the players without running into the 'why would I go along' problem, since they solve it explicitly.
Alright, youse mugs
Part of character creation mandates that the character must end up 'in jail' 'part of the mafia' 'in a specific diner on 9:43pm on a sunday night'. Then they get involved due to that fact. The Mob Boss makes them an offer that, as wiseguys, they can't refuse. They're let out of jail and given magical bomb collars (that are NOT plot devices and can be removed given the right mojo) that force them to act as shock troops for the Empire. Or the jail is attacked and they have to survive goblin attack on the town which by the end of it leads into more plot etc. Everyone in the diner is shiftless and at loose ends and so when a 'gal' comes in cold and wet and talking about the headless Rider, they end up drawn in. Etc.
Something about character creation puts them in a position to get hooked, and the hook is 'forceful' - refusing it is less likely than a simple job offer or request.
Jim the Paladin wakes up in a jail cell and breaks out. Tim the Rogue is being carried on a stretcher towards the Incinerator. He fights the guards and frees him, and him and Tim are now a team with the goal of 'get the heck out of here'. They run into Bertrand the Ranger who has been enslaved in the kitchens in the next room, and after that they rescue a Wizard trying to fight off a [Monster] in the entryhall.
By the time they break out, they've learned the nefarious plans of the BBEG, bonded together, and all have the goal of 'revenge on that BBEG'. Not that you might not need to hook them back into the main plot if they instead decide to go start a bar together or something (BBEG burns down their bar, king offers them money to start a bar if they fight the BBEG, etc).
The Ideal First Session
The characters need to be introduced - The PCs need to have something highlight who and what they are, even as simple as a one-sentence description and a name.
Something Awesome needs to happen - If you can manage the PCs being the ones doing it, that's even better. But an Airship smashing through a castle wall, a bad guy swearing revenge, or an awesome bare-knuckle prisoner breakout/rescue scene. Something that gets people excited.
Some kind of foe needs to be introduced - Even if it's just a small starting adventure with a poor villain, Bogrob the Goblin Shaman needs to be mentioned in the first session. You can always 'move it up' to a larger foe as the story continues, but without a foe, stories with protagonists.. dwindle.
Someone needs to win something - even if it's just the favour of a barmaid. Plot exposition is important, but without a victory of some description, even one by the enemies over the PCs, people won't remember any climaxes from the first session and be less excited about the second.
The tone needs to be set - this is probably the most important. If you want Swashbuckling Heroism, swashbuckling needs to happen, so does Heroism. Ideally this is the PCs. But if not, still needs to happen. If it's Noir, there needs to be rain, damsels, chain-smoking, old-school black and white film techniques in the description, and trenchcoats. If it's dark and gritty urban fantasy, there needs to be lots of mystery and things left unexplained, horrible things happening to people or characters, etc. Tone, set, important.
Characters each need to do something that shows off their nature - saving someone, stabbing something from the shadows, stealing something, casting a powerful spell that has foes cringing in terror even before it tears them apart, so forth. You need to get a read on what kind of acts they want their character to perform, and set things up so they CAN (if they don't bite the first hook, lay a different hook - you likely read the character wrong or they missed the hook) do the thing. One per character. Important.
There needs to be a mix of action, investigation, mystery, non-combat character actions, and combat character actions - a lot of GMs use the first session to give a ton of backstory exposition, sometimes through a mouthpiece NPC. This is a really terrible idea. Could not be worse. Mix it up. Have a small fight, the PCs walk across town and interact with a baker and a merchant, they get told tantalizing hints about the plot from a guy, their contact is gone and they search through his things and find a scrap of red paper embossed with a seal, etc (keep in mind the Three Clue Rule).
How to Introduce NPCs 101
Make them people, with their own lives. Nothing sets up a character like having the PCs show up as he's wiping down his bartop, and he's not exactly keen to see them. Small details, like greasy white mutton chops, smokes a cigar, old and doesn't give a darn, wears only the finest pressed robes, bit of a ponce. Don't be afraid to give them negative qualities.
Finally, make their motivation pretty obvious. They are there for a reason, like to get paid, to get the PCs to do what they want, etc. Sure, a good liar gives no sign of that - make all your NPCs bad liars. Save the really really good liars for very rare use, when they betray the party and gloat about how the party bought into all their bull. People will get really mad, it's great.
So, in short;
- Simple physical distinguishing characteristics
- Positive and negative qualities
- Don't feel the need to lecture the PCs for hours on random things like a quest npc in a videogame
- Have a reason to be talking to the PCs, like giving them a job or serving them beer or something
- If they approach for 'no reason', always make them have an ulterior motive the PCs find out pretty fast