If a fella goes through the sandpaper grits, say 150 to 220 to 320 to 400 to 600, and at each grit he makes sure that scratches from the previous grit are removed, by the time he gets finished at 600 grit there aren't any visible scratches. Any finer grit than that is probably wasted if he's working walnut. Certainly you can go finer than that, and if you are wet sanding, the dust/oil will go into the pores of the wood and eventually close them up. You could also accomplish that with 400 or 600 grit. The trick is to not pull the dust/oil mix out of the pores when you wipe off the excess oil.
As for which oil to use, in the past I used Boiled Linseed Oil. Nowadays I'll usually grab the can of Minwax Antique Oil. It's similar to tung oils and danish oils, in that they are a mix of Mineral Spirits, BLO, and varnish, though the percentages of each vary by brand. You don't even need to buy a can if you have all 3 of the ingredients mentioned. You can mix up your own, and you can get the recipes off the internet. None of these will be waterproof, but they will be water resistant. I use the Antique Oil because a fellow I know that taught woodworking for 35 years said that he always thought that Antique Oil gave the best finish. That was good enough info for me. Is it the best? Heck, I don't know, but I do like using it. It's faster than doing the stock in BLO and it gives a nice soft satin look finish (which probably all of the wiping varnishes/tung oil/danish oil will give). And you can wet sand with it. The more coats, the more shine. The first coat looks terrible. Second coat looks good, and successive coats look even better. Not much point in going past 5 coats or so.