I specialize in repairing old houses, and it's common for basements to be full of junk. I also work by myself.
The most difficult part is convincing the owner to get rid of the junk. They all think it's just a matter of "organizing" the stuff, but in my book, they either commit to discarding stuff, or they need to find someone else to help (this is no judgement: I come from a family of hoarders and love them very much, but talking to a hoarder about their stuff is a no-no to me.)
The second most difficult thing is assessing the amount of work. It's not just a matter of hauling the junk, but that you'll find things that can't be disposed easily (ie solvent-based paint, dehumidifiers, etc.), stuff that should not be thrown away (ie good tools), etc. You will do the first 80% quickly, and the last 20% will take forever.
If you have more than 5 yards of garbage, the easiest is to rent a dumpster. These can go for $500-$1,000 depending on the region, size, weight, etc. I've done cleanup jobs where the dumpster fees alone were >$5,000. If you cannot rent a dumpster, you need a plan for disposal.
Once you have a plan, buy a Tyvek suit, a P-100 mask, a 30+ gal rubbermaid can, contractor bags (2 mil min), lots of gloves, and a case of bottled water.
During the cleanup itself, the trick is not to go the route of wanting to bag everything at once, carry everything out, etc. Instead, fill one bag and carry it out. Have a drink of water. Then go downstairs again. Repeat 100+ times.
As you find hazardous materials, put them to the side, and find out how they are disposed of in your locale.
Once all the junk is out, mist everything with water to remove the dust. Then it's time to do repairs, like removing mold (bleach with backpack sprayer), repointing foundations, repairing windows, etc. And the plumbing you mentioned.
Depending on the size of the job, this can take from 2 days to 2 weeks. It can be done, as long as you pace yourself and have the budget. The biggest I've done is 100 yards of garbage by myself. Took a week.