Hi Jim,
That's entirely normal and good practice and pretty well documented in the pattern books.
The only thing I have never done is use the default database as a standalone installation although it should be possible. Many people use their own database deployments as they will already have established backup and DR processes.
It's good practice as you can expand individual tiers without changing affecting the overall architecture. For larger deployments you can even separate the management (CMS and supporting servers) from the reporting servers but that may be overkill for you.