Add JRE to Base 6.1

Which JRE do I need for Windows 10 PC and which one for an Ubuntu PC

You can use any version of JRE with LibreOffice in Windows. For Ubuntu you should install OpenJDK from repos of Ubuntu

You can use any version of JRE with LibreOffice in Windows

… but make sure that you use 64-bit JRE for 64-bit LibreOffice, and 32-bit JRE for 32-bit LibreOffice.