Its a king water stone. You "can" use oil, but water is best to get the slurry going. So, just use water imo.
Its not expensive, those sell for like 30 bucks, but they work really well, and are some of my favorites.
Soak it for a while, I just leave my stones submerged, but that does soften and shorten the lifespan of them. But i hate waiting.. 800/4000 never made much sense to me, but I would honestly buy a 1000/6000 stone set to compliment. 800 -> 1000 -> 4000 -> 6000. I normally just go 1000 to 6000 wtihout any issues, but a step between would be ideal. Amazon sells them cheap enough.