I would avoid using a liner. It will most likely impact the very fast drainage most herbs prefer. Cedar treated with a mineral oil can be expected to hold up very well.......you should get a good 10 years or more from these boxes, especially if raised up off the ground.

And skip the gravel as well......it's a very hard to break myth that this helps with drainage in a planter or other container. It does quite the opposite!

So just some small holes in the bottom and then mesh liner just on the bottom?

Yep!! But make sure you have plenty of drainage holes. Drainage is critical in any container gardening situation (including planters of any size) and with herbs or other plants that demand fast drainage, of even more importance.