Read an article about adding patina to suiseki by putting them on your bench and watering them daily. Something about getting wet and drying daily.
What do you think about the stone on the right. Newly aquired. Is it suiseki?
I'd go with vaseline or other petroleum based jelly. It sinks in reaaaally well in dried rock. Otherwise, there's always clear engine oil. Just a small soak should suffice.
Hand rubbing is fun, it works, but after a while, the skin flakes will build up in the rock pores and it will start to smell like wet feet. Not something I'd want to touch daily.
Oil will ruin the patina. Been there, done that. And that's not just my experience. They look good for a while, but eventually the oils attract and hang on to other debris that make things look cloudy. It's hard to get back to the original look of the stone when it gets to that state, let alone a patina-ed look.
The Japanese term for aging a stone is yoseki. Water and sunshine are part of it, but so is handling the stone. The miniscule amounts of oil on your hands won't have the same impact that directly applying other oils will. How you age a stone depends on the mineral type. I collected a lot of limestone when I lived in Virginia, but that type of limestone doesn't do well out in the weather like limestone from Italy. So just like w/trees, practice on the inferior material. Also, photograph and compare the stones from year to year. If you think it's hard to see the growth in a tree from year to year, watching a stone age is even tougher.
Also, not all stones need to be shiny. In fact, if you look through albums from some of the suiseki shows, you'll notice that not all stones develop the same type of patina. And that's just fine.
As far as the stone on the right... it can probably be suiseki. The colors are good and so is the profile. You can treat them sort of like bonsai. You want the stone to visually invite you into the image. The stone should really only have one flat side (if the back of the stone is flat, it lacks visual depth, like a bonsai tree w/out a back branch), and be roughly an irregular triangle. There are lots of other "rules" out there that are mostly based in good artistic principles.
There are a lot of visual traditions that go along with "suiseki", but there are many viewing stone visual traditions in other countries too. For that reason, I like to stick with the term "viewing stone" instead. It removes those pre-supposed visual traditions from the mind, and lets the viewer take in the stone for what it is, without trying to apply aesthetic concepts that may not work,
Having said all that, most, if not all, of my stones are flawed in some way. But I enjoy them for what they are, flaws and all. That doesn't stop me from continuing the search for the perfect stone, and picking up many that aren't perfect along the way.