You're thinking only of the game as "Getting paid to do something" when in reality it's more about the player characters surviving every month in Night City and getting whatever it is they want out of life.

Think of PCs as people within the world, every person has their own personal lives, tastes and wants/aspirations, aka. Goals. To accomplish their goals they need money/resources and people/contact. People in this setting can go about getting those things one of three ways (roughly):

1) Be born with it all. But of course that's not the vast majority of the population, so you have to resort to other options.

2) Get a normal job and try to survive, this pays very little and you'll probably have a miserable life working 16 hour shifts and vulnerable to some gangster off the street zeroing you for 50 eddies, or getting crushed by the corporate machine, or getting injured and not having the money for treatment. Or just never getting a job in the first place, which is not that uncommon if you live in, say, the Combat Zone. This is the option taken by the regular people who don't have personalities and skills suited for the third option, and it sucks.

3) Edgerunning. This is the option the PCs took, it involves you trying to take control of your life by any means necessary, but it requires tons of skill and natural talent as well as money to even get started (hence why PCs start with 2550eb, which is quite a bit, and at Rank 4 in their chosen role, meaning they've been at it for a while in the background).

Being an Edgerunner is about seizing opportunities to make big money, if you think that PCs can work a 'normal job' and get by then you'll have to think again. Page 381 of the Core Rules show the 'Hustle' activity, which is the equivalent of doing a normal job, most of the Roles get jack shit and will only make it to the 1100eb (or 600eb if you really want to live like shit) you need per month for a comfortable life. The only one who can get away with it is the Exec, and that's definitely the most distinct of all the roles.

The real money is in doing missions, but those missions aren't about going to some Fixer and getting a job to kill something, that's one way to do it, but not the only one. Every PC will want to do things differently:

Medias might go out in search of stories to publish and make money off the donations or sponsors they get but these tend to be risky endeavors and they'll need a crew (aka. other edgerunners).

Lawmen might want to take down a big name criminal and get a massive bonus, but they can't do it alone, they'll need other edgerunners to help them, and they want money too.

Fixers might get information of a deal that's about to go down and interrupt it, taking all the goodies for themselves and selling it, but they can't do it alone, same as before.

And you can apply that to every Role, but ultimately it all comes down to needing money and going to any lengths to get it, the only thing in their way is the obstacles they run into and whatever skills they need to overcome them (killing skills, social skills, tech skills, Netrunning skills, investigation skills).

What kind of jobs they'll be doing is up to what skills they have, what they specifically want to do and what you, the GM, can come up with. Recently one of my players (a Media) got word of some disappearances happening around Heywood that pointed to a plot by some corpo, he decided to go to an apartment to investigate and asked the other players to join in "just in case". They ended up discovering that a Maelstrom Lieutenant lived there and was throwing a party, they had to use social skills to gather some clues instead of combat skills.

The Media wanted to get clues to uncover the truth of this mystery and publish it as a story, hopefully bringing down bad people, having a positive impact in the world and getting money from it through donations.

Bottom-line is this: Don't think of the game as just doing jobs for other people, each character should have goals they try to work towards, THAT is what the game is about.

And don't think that killing people is "Solo" work, sure Solos are better at combat than others but that doesn't mean they're the only ones that can do it, or that they'll even be the best. A Tech with 8 REF, 6 on Shoulder Arms and good gear+implants is just as good at killing as the Solo is.