How old are all the players? How old are you? I could have said how mature are you, but no one says I'm totally immature. Gaming can be for almost any age of player, but the game is going to be quite different. Your ancient runners, like myself, often want different experiences then high school runners or college runners.
Just basing this off your description I would suggest highly physical jobs in low tech areas. I certainly can't say for sure but it doesn't look like you have a hacker or technomancer so that can limit your more complex jobs. Doesn't have to, but it certainly makes them harder to pull off.
Suggested runs with that team
Combating a ganger problem in the neighborhood. A local charity has had enough and needs a small group of runners to discourage a small gang from harassing the kids at the local school. PCs can negotiate or go to war with the gang, lots of options in between.
Transporting "packages" around town. A local organized crime syndicate or corp needs the runners to move packages place to place without getting jacked. Opportunity to meet new and interesting people, gangers, rival syndicates, rival corps, cops, etc. Can have additional complexity, maybe the PCs are transporting something they are morally opposed to and one day by misfortune figure out what that is.
Running a protection racket. The local bar tender doesn't want to pay and he has some friends that the local criminal organization doesn't want to cheese off. However if deniable assets do the damage then they can make their argument without getting entangled.
Running protection on a small time operation. The runners are hired security. A small local criminal group made some enemies recently and need a little extra muscle to make sure their cash cow operation doesn't get disrupted. Its only after they take the job that they realize maybe they don't want these guys protected? Maybe organ leggers, a slavery ring, forced prostitution... something even less savory.
A fixer needs runners to extract a small time local figure (could be a drug lab chemist, a lower level wage slave, a rivals kid, etc.) and return the target safely to point B. The target is not willing to go and has some protection.
Hopefully that is a few good starting points.
Talk to your player, mention that fighting everybody is eventually going to lead to him either getting killed or not getting any jobs. Rep is everything in this biz.