"Stone" could mean a hundred different things. Specifically, what material will you use and what method of construction?

Sorry to not be clear. I have blue flagstone (similar to this: http://hammerheadstoneworks.com/wp-content/uploads/sites/5/blog-images/bluestone/blue-wall.jpg). It will be a dry stacked wall - no mortar. Does that help? Thanks!

Since the wall is dry stack (it's flexible -- as opposed to mortared, which is rigid) it can move with frost without danger of cracking and disintegrating. So there is no need to go down below the frost line ... especially 40"! If you dig a trench just deep enough to hold the wall in place (4" to 6") that will be sufficient. 30" height of retaining wall for a raised bed seems high to me. You would need to make the wall quite thick (half the height) in order for it to be stable. I would consider a lower wall if you could.

Thank you for the response! We are making the wall 30" because it will run across the back of our property - which is lower than our backyard neighbor's property. Building it at 30" high will, once full of soil, have the planting area level with their backyard and give us a bit of a visual screen. It also will make the patio (that we are putting in front of the wall) feel a little sunken which is what we want. I was planning to make the wall 12" thick but will make it a bit thicker given your advice.

Should I sink the first course or doesn't that matter?

Is this going to be such that after you fill the wall, you're not going to see it because it faces the backyard neighbor's property? Can you show the area? I would not only sink the wall but put batter (face slope) on it. It will probably help you to study some Google images for "retaining wall batter."

This isn't really a DIY project. If the worst thing that happens when the wall collapses is that it makes a mess, you'll just have to clean up the mess. Otherwise, the wall is within the specs for interlocking block walls.