If the solutions can be mixed safely without problems, you could just cement out values and treat the gallons and gallons of waste solution.
Treat any ammonium solutions separate from the other solutions, or acidic salts.
During the process, you will recover any values from the previous mistakes and clean up the toxic lab.
Now after seeing that recovering these metals from solutions and then refining them it is not as simple as presumed, we can go back and start from the beginning to get it right, going back to studying and learning from our mistakes, before jumping into another mess unprepared to deal with it.
Then I would begin to study on one of the simple materials like memory fingers, karat gold, or sterling silver.
Working with easier scrap that involves less problems to deal with and will be easier to learn on.
Study each process well to get a good understanding before you begin.
While studying Hoke's book. work with the getting acquainted experiments, to gain a better understanding of how the metals react in different solutions or conditions, you can do these types of small scale expieriments with other materials such as electronic scrap to gain a better understanding.