How should I prepare the base of a small paver brick retaining wall
A good starting point would be to plan on burying one course on a minimum of four inches of compacted gravel. The buried blocks don't buy you much stability in that configuration but they will help keep the wall from sliding forward and prevent the ground washing out underneath the wall, which is unsightly.

The gravel base must provide enough drainage to prevent your wall from becoming a bathtub. Barring truly epic monsoons or snow melts a modest depth should suffice. The base, by the way, should be twice the thickness of the wall. I doubt that's an issue since a ditch narrower than 8" would be a real hassle to shovel or tamp down stone in.

That basic plan should be modified by the local frost line, soil composition, and common sense. If an extra couple inches will get you below the frost line that's good insurance against heaving. If going below the frost line means digging an extra two feet that's a good reason to stop early and have a beer. Remember, you never get perfect compaction even with a machine. An exceptionally deep base that's 90% compacted will still settle a couple of inches.