You are correct in that you will need a JRE package to run any Java application.
Since you say you’re running on an embedded platform I assume that the Java application you want to run has no GUI. In that case, you will be fine with openjdk-6-jre-headless. This is explained on the openjdk-6-jre-headless package page here “Minimal Java runtime – needed for executing non GUI Java programs”.
As you can see from the debian package details page, openjdk-6-jre-headless depends on openjdk-6-jre-lib (among other packages), so that will get installed either way.
If however the Java application you want to run has a GUI, you will need openjdk-6-jre instead of openjdk-6-jre-headless