The Never Ending Game
Okay, it's somebody's life you're dealing with here. The players are acting out someone's life in a cyberpunkish/fantasy setting. And that person goes on a mission -- a few plot twists later, he's been paid and the run is over until the next game session when another mission comes along. Nothing that happened on the first run will affect anything on the second run.
How many people's real lives are like that? Does your life have definite starts and stops where nothing carries from one part of your life to another? No.
As a GM, you have the ability to make the players feel as if they actually are experiencing someone's life in the Shadowrun game world. Now I don't mean shoot them in the arm when their character gets shot in the arm (no matter how tempting it may seem at the time). I'm talking about making the players feel as if their characters actually exist in a real world.
But to do that, you're going to have to do a lot of work up front.
Back when I GMed that TSR game (back before they started ing every fifth word in their books), my preparations for each game session would consist of three steps:  draw a map,  find some interesting monsters, and  people (monster?) the creatures in various locations in the map. This would be done the day before the game session or even the day of the game session. Sometimes it was during the game session. But that leads to meaningless adventure after meaningless adventure. They could have been played in any order and nothing would have changed. They could have had any type of character and nothing would have changed. They could have skipped over the adventure and -- everyone together now -- nothing would have changed.
There's a better way.
To give the players a sense of a real world with real people, you need to learn the magic word. That word is "foreshadowing".
Foreshadowing - showing or warning beforehand.
To use foreshadowing, you need something to foreshadow. Create a goal for the campaign, or a milestone in the campaign. Or even an event in your campaign that will take place sometime in the future. Write out this run and a few notes about the runs between this one and that key run.
Plan about six runs ahead of your players. This allows you ample time to start introducing something about runs five or six in your current or subsequent runs to lead up to the key run.
Example: The key run is an adventure where the shadowrunners have to guard a Mafia boss for a week and the Mafia boss is going to be the target of an elite assassin in that run. We'll place this run about five runs after the current run the characters are at. Start dropping hints about trouble in the Chavez Mafioso family weeks ahead of the bodyguard run. A cop or snitch contact mentions something in passing, the characters hear of a drive-by that wounded one of the Chavez lieutenants, or one of the Family's protected establishments goes up in flames.
The secret to doing this is to know what's going to happen next. Not "knowing what's going to happen next" as in controlling your player's character's lives, but knowing how events in the world are going to play out regardless of the character's actions. We know that the UCAS 2056 election is rigged, and we know the course of the 2057 election - and regardless of the character's actions, things will happen the way they happened.
Once you plan out what's going to happen (say, a war between the UCAS and the CFS when the UCAS decides to take back California), you think about the key points in your campaign that lead up to the war with the UCAS and CFS. Then just introduce these points into your campaign.
Next: Some more information on how to construct an on-going campaign.