I have been making end grain cutting boards for friends and family for years. I did a fair amount of research before starting. What I learned from woodworking forums is that what helps make wood "food safe" is the moisture content. Or lack moisture content. The lack of moisture makes it difficult for bacteria to grow. My cutting boards start at about 6 to 10 percent moisture content when I build them.
The best oil is a matter of choice, but a few rules I picked up are to avoid oils that can go rancid and avoid oils that harden. Going rancid is self explanatory. If the oil hardens then It can only sink into the surface of the wood. Every application of oil after that is on the surface building up a thicker layer. Once you cut that hardened film layer the seal is broken.
My preferred method for finishing a new board is to flood the board with food grade mineral oil repeatedly. letting the oil soak in for a few hours. I repeat this process at least 5 times. The next step is to melt beeswax into some mineral oil. My recipe is 3 parts oil to 1 part beeswax. This is just approximant, I'm aiming for a paste consistency. Maybe a little thinner than chapstick. I add a few drops of peppermint essential oil but that's just to jazz it up a bit because I give a small jar with the board as part of the gift. The wax probably isn't necessary but it does greatly increase the time between applications. Put on a generous coat rubbing it into the grain. The paste is thin enough that rubbing it in will melt the wax allowing it to really flood and fill any small cuts or pores in the wood. Let it sit for about an hour and the oil will soak in while the wax hardens. a quick buff and you're done. My gift boards get 3 or 4 more coats of the mix followed by a buffing with a power buffer. With some work I can get them looking glossy, probably overkill because I have been told more than once that the idea of taking a knife to it seems a shame.