Your players are right

Yes, that's probably not the answer you wanted to read. But 3,000 nuyen is pretty much the baseline for all shadowruns, even those without any security risk at all, like grabbing someone on the airport and bring to downtown (taxy job) so they can avoid the paparazzi. Even a job as simple as hacking into a security terminal to scan for a list of names has enough risk to be considered a job worth at least 6,000 nuyen.

Following the guidelines on the Core Rulebook (page 375, Run Rewards), we have a base payment of 3,000 nuyen, with the possibility of increasing this value by 100 nuyen per net hit on a Negotiations test.

$$ \mbox{BASE COST} \qquad \mbox{ 3,000¥} $$

Then, depending on the job, this base value is multiplied by the modifiers on the Cash Rewards table (page 376):

This means if they face gangers who have a dice pool of 8 dice (this is fairly low for opposition), the payment for the run already tripled and whatever payment of 3,000 nuyen now should be 9,000 nuyen per runner.

If they face a group of Red Samurai and are outmatched two to one (8 samurai vs 4 runners), then the payment should be much higher, as samurai are professional rating NPCs (+1 modifier) and their dice pool is 12+ (+3 modifier), for a total of 15,000 nuyen per runner (not including whatever is the result of the negotiation check).

See how things scale quickly?

I have GM'ed shadowruns where the calculated payment was in the 40,000+ per runner, because it was a multi-part job and nearly all modifiers on the table applied for that specific job. And it was all finished in 3 days of in-game time.

The calculation of this payment is in the GM's hands, though most (if not all) published missions already do this math for you.

Of course, sometimes you will not know how dangerous a job will be until things go south and bullets fly everywhere, so runners will be offered a low payment, but the job proves to be much more difficult than what was agreed earlier. But that is better covered on this question.

Why hire shadowrunners? They are expensive...

When a Mr. Johnson decides to hire runners, he doesn't want anyone for the job, he is looking for professionals ("get the job done"), he is looking for discretion ("no questions asked"), and he knows he has to spend extra cash for people like that. If they wanted anyone who could do the job, he wouldn't look for runners, any ganger could do, any cop looking for an extra cash would do, anyone who usually does for a living, whatever the job requires to do, would do. That is not the case.

Remember, shadowrunners are not wageslaves, they are not on the safe job industry, they are risking their lives. So why would you risk your life if you wouldn't even be able to pay your rent with the payment for it? Why risk a bullet in the head if you couldn't even pay to fix your damaged cyberwares?

The GM controls the cash-flow

Who, how and when the player characters are hired for a job is completely into the GM hands. I have seen shadowruns being done once a month, once a week, once every other month, and as soon as the runners are free for another job, sometimes even doing two jobs at once. But this is all dependant on the GM and what kind of gameplay you guys are looking for.

It all makes sense in the setting, some runners are desperate to earn money and become rich as quickly as possible so they can retire (or spend it all on luxury cars), while others take things slowly, avoid exposure and keep a low profile. Jobs can be difficult to come when your face is all over the matrix shooting bullets against innocents, by the way.

As the GM, you will have to ask your players what pace they want for their jobs, this is not even metagaming, they can discuss that with their fixer(s). If the runners are not available for a job, a fixer will look for someone else who is. There are always a group of runners looking for quick cash, that could be your group, or another.

The Ability Check is a DM decision

Page 174 of the PHB covers Ability Checks and how they work (emphasis mine):

The DM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure. When the outcome is uncertain, the dice determine the results.

The player comes up with the narration of what they're doing and then the DM determines HOW or IF success is determined.

But why can't the player suggest?

The rules (Basic Rules, 58) also account for this.

Sometimes, the DM might ask for an ability check using a specific skill--for example, “Make a Wisdom (Perception) check.” At other times, a player might ask the DM if proficiency in a particular skill applies to a check.

So, they absolutely CAN, if that's the way the table environment is set up. But it is the DM who has final determination on what ability that action described requires. It may not be the ability someone is proficient in, but that doesn't mean it's unfair. The player may have a good reason for wanting to use that ability - and if they narrate their action appropriately it may work the way they want. But the DM determines if, when, and what the player will roll to determine success.

The key is really in how they describe what they want to do. Not everyone is comfortable with roleplaying, but all players should be able to describe what they're doing and HOW they're saying something (but not necessarily WHAT they are saying.)

Being a good DM is listening to players and knowing their strengths and weaknesses (both as characters and as players.) Helping guide the player to the narrative they're trying to create is absolutely fine! Just be wary of twisting a situation so that it's always at their best. There are times when that's fine, but there are times when what they're trying to do really only works one way and the DM can make that call, too.