I had success with the following:
1) Glass bottle, ideally with flat sides. If you have a round bottle you may not be able to see the ferrofluid due to diffraction.
2) A solution of ~25% distilled water (a.k.a. deionized water) and ~75% of store bought isopropyl alcohol at 91% concentration. That means that ~70% of my solution was actually isopropyl alcohol. I eyeballed the ratio between the water and the isopropyl alcohol, those numbers are likely to not be exactly correct.
Procedure that I followed:
Add some isopropyl alcohol to the glass container. Then add some (or all) of your ferrofluid to the container. Then add some water to bring your isopropyl alcohol concentration to about 70%. Next, use a magnet to settle the ferrofluid to the bottom and then remove the magnet. If your ferrofluid has little bits that are floating, then you need to add more water. If your ferrofluid looks too stringy then I would add more alcohol. When I was done the ferrofluid had zero staining, like you see in the videos online, except for in a few spots. I think for better results I would need a higher quality glass container.
notes: Don't put too much ferrofluid in your container, otherwise you will have an uninteresting blob. I recommend using gloves. To clean the ferrofluid stuff off my hands I used warm water, laundry detergent, and lots of scrubbing with a towel. If you mess up, you can use a magnet to hold your ferrofluid in place while you pour off some of your suspension fluid. In addition, you can use a straw and your thumb to pipet some of the ferrofluid, however some will get stuck in the straw, so I wouldn't do that unless you have a bunch of ferrofluid. Finally, I only finished like 30 minutes ago, so I hope it will all look good tomorrow. If something bad happens I will make another post.
notes, part 2: If all you want is a cool desk toy, then I recommend just buying one of the pre-made ferrofluid toys online. (I saw some for ~$30). You will get a lot more ferrofluid for your money if you buy just the ferrofluid, however making the toy is a bit of work.
edit: no combinations of the following worked for me: acetic acid, hydrogen peroxide, pep plastic.