While a plain Debian GNU/Linux (choose no tasks with the installer and what you get is pretty lean) should do the trick, why duplicate work? Have a look at the TurnKey Linux Virtual Appliance Library (it's Debian-based). Especially note the Development section:
Customize an existing appliance or develop a new one
TurnKey is designed to be easy to build on using TKLPatch, a simple customization mechanism.
Example customizations include updating a configuration file, adding data files, adding a package and even creating a brand new appliance leveraging a generic appliance such as Core, LAMP, Rails, etc.
You are free to develop TurnKey appliances for private use, but we encourage everyone to share their results with the community. That way we can harness contributions to improve future versions of TurnKey.
Once we add a new appliance to the project we assume the burden of maintaining it at the appliance level with regular updates. This frees you to focus on more interesting tasks (e.g., improving quality of integration, software sub-components).
(It surely depends on what you're up to, but this could be a good fit.)
Apart from that, you could have a look at SUSE Studio to generate a JeOS image to underpin your application.