Which JRE should I install?

I recently downloaded a free app that creates patterns using specific preset mathematical formulas. The author said I needed to have the latest JRE installed from the Sun site. I went there, but was frustrated to find several Windows JREs. I found two possibilities and don't know which one to install. One is described as the "offline" version and the other is described as the "kernel" version. There were others at Sun, but these two seemed to be the most likely. Any tips?

The "offline" version is an installer program which you download and then run. It is probably the one to choose.