Maple supposedly kills some bacteria. You should make them out of a closed grain wood, but there's plenty of oak, mahogany and other open woods used.
We make them out of maple, cherry and walnut primarily and do 20 or 30 cutting and serving boards a month out of cut-offs.
Some people will tell you to alternate boards so that the rings run up on one and down on the next, but it really doesn't make any difference. If you're concerned about it, use 1/4 sawn.
If it's a meat cutting or chopping board, then you should make it out of endgrain. This will last much longer and won't dull the knives so fast. For bread boards and vegetable cutting boards edge grain is sufficient and for serving and infrequent cutting, face grain is okay. But remember that cutting on face grain is going to very noticeable and if you're showing off some figured wood, it'll be all scratched up quickly.
Of course you can resand or scrape the surface every so often to restore that pretty wood.
I prefer walnut oil because it dries and looks a little better, but lightweight mineral oil, (butcher block oil) works very well and we use it probably half the time. You can also use regular mineral oil as stated. The only real drawback to regular mineral oil is that it takes forever to halfway dry and will weep for months if the board gets warm. The lightweight will more or less dry in a couple of days and doesn't seem to weep.
I prefer Titebond III glue for these, but one of my guys prefers the Titebond II. We both use our boards and I can't recall ever having one fail.