Blind/buried vs. through hole vias?

Blind and buried vias add a lot to the cost of a multi-layer board, and are only used on high-density, high-performance systems. The increase in cost is because the layers have to be drilled separately, assembled, and then the holes are plated. Blind vias are sometimes back-drilled (the unwanted plating is removed with a slightly larger drill from the back) which reduces the cost, as the layers are stacked before drilling.

Cost..

Here is a small example, I hired an inexperienced guy, he made a 4 layer PCB design, 30x50mm board. I sent to get a quote, I get a quote for 2K USD for 20 pieces, I naturally objected. They have said, this has buried vias. Later, I changed the design sent the gerbers back, price was 150$ in 5 working days.

Unless you have BGA package, don't use any via other than through hole.

Do not use Blind/Buried vias. You'll always find a cheaper way to finish your board without using them. That's what I used to do.