Install mainstage only?

Here's the system requirements:

Minimum requirements to install all applications
Mac computer with a 1.25GHz or faster PowerPC G4 processor (PowerPC G5, Intel Core Duo, or Intel Xeon processor highly recommended)
1GB of RAM (2GB or more highly recommended)
Display with 1024-by-768 resolution (1280-by-800 or higher recommended)
Mac OS X v10.4.9 or later
QuickTime 7.2 or later
DVD drive for installation

You can't install just the Mainstage application by itself (i.e. without any of the content). If you check just the Mainstage checkbox in the installer it will install the app and the minimum required content, which is several GB's I believe. However, it can be easily found and deleted.

Good luck.

Save your time: it won't work.

The limitation is not only based on the CPU clock speed, but also on the memory and the video card.

With 500MHz you probably have a PowerBook G4 or an even older PowerBook (FireWire) with a G3.

A G3 is not supported at all by Logic Studio, even if you bypass all checks to avoid the launch, it won't work.

So we have the G4 PowerBook with 500MHz (the very first one). It supports up to 1GB of memory, which is the VERY bare minimum for MainStage. Sampler stuff (like the piano) probably need more. The graphics card also only has 8MB, not the required 64MB and Quartz Extreme Support.