You are liable to get a lot of different opinions as everyone has their own idea.
I use different hard woods primarily oak, maple and walnut. I prefer mine about 5/8" thick. I would think they would need to be at least 1/2" but could be thicker.
I also finish mine with mineral oil. I soak the trivet then let it drip dry, wipe off any excess and after it dries buff it with a brown paper bag.