If you want tip-top yet practical material for pieces, it's mammoth ivory, I don't include gold, diamonds, etcetera.
Ebony/boxwood is fine for wood, as is red sandalwood/boxwood, and rosewood/boxwood. There are others, like purpleheart, that rarely get used for pieces but seem to work well enough.
Boards can use many fine materials from stone to wood and be very practical. The variety of woods used for boards is impressive.
Set up only at home? Traveling? By water? Playing friends? Playing in tourneys? What kind? Playing kids who just finished their PB&J before the round started?
Best depends on use, and has to consider cost. If you can afford a couple thou for a set you can afford different sets for different purposes. If you are like the rest of us...
I'm not the richest person in the world, but I want something that isn't made in a sweat shop in china.
You're in luck. All the sweatshops are in India.
Do you have a $ range in mind? And a place and purpose for the set?
They're in India? Well now I know. About 50-70 bucks
There are a lot of good, low cost wood sets. I think chess.com has something arranged with House of Staunton but you would need to verify that.
What do you like in wood? Heft, color, shadings? Does the wood have to be the solid color or can it have character?
I like a dark shade of red, and I just like solid colors.
Here's an affordable knockoff of what the pros use in their tournaments. Not a great set but a perfectly good one:
Just one of many options. Emphasis on the many.
What is the best, highest quality for chess boards and pieces?