You are correct. If your installed world of warcraft is at patch 4.0.3, then you should not run any further installers. If you do the Digital Online Upgrade, it will automatically upgrade your account, and there's no need to update your client.
To clarify, because there seems to be a bit of misunderstanding on this point, there are two different 'versions' of World of Warcraft. There's the client version, which you can see when you launch the game in the bottom left corner, and there's the version (really, the expansion level) in your account. No matter what expansions you have in your account, you must have the latest version of the game installed (currently 4.0.3) in order to play. If you have that version, then you have all the game data necessary, regardless of expansion level - any account can log in using that install.
What that means for you: As of patch 4.0.0, any new install can be done in a few ways:
- The easiest way is to download the 4.0.0 installer: https://us.battle.net/account/downloads/WoW-4.0.0-WOW-enUS-Installer.exe
- If you don't have a good internet connection, or you do have install media (CDs or DVDs) for any previous version, you can use them. Once you do so, the patch process will begin, and will update your client to 4.0.3.
Either way, your client is now fully updated. You need to do this whether your account is classic only, or if you have BC, or Wrath, or even the Cataclysm Digital Download.
If you later update your account with BC or Wrath, you do not need to install or update using any installer or install media. Your client is already at 4.0.3. Installing with Wrath DVDs will partially overwrite that with version 3.0.0, or BC DVDs will overwrite that with 2.0.0, and that will result in a corrupted install.
If you later add the Cataclysm Digital Download, you must log in to your account once. This will tell the client that your account has Cataclysm enabled, and will tell it to begin downloading data as it becomes available. This will happen whenever the game or the Launcher is running.