Primary source for this information comes from Apple.com.
Requirements for Mac OS X v10.3
Mac OS X 10.3 works with these Macintosh computers:
Power Mac G5--all models except Power Mac G5 (Early 2005), Power Mac G5 (Late 2005) which use Mac OS X v10.4
Power Mac G4 or Macintosh Server G4--all models
Power Macintosh G3 or Macintosh Server G3 that have built-in USB ports
iMac--all models released in 2004 or earlier
iBook--all models except iBook G4 (Mid 2005) which uses Mac OS X v10.4
PowerBook G4--all models except PowerBook G4 (Double-Layer SD) which uses Mac OS X v10.4
PowerBook G3--Bronze Keyboard models only
Usually, the earliest version of Mac OS X that a Mac works with is the version it ships with.
Computers with processor upgrade cards are not supported with Mac OS X. Although Mac OS X may install and appear to work normally on some computers with third-party microprocessor upgrade cards, Apple does not provide technical support or assistance for Mac OS X when used in this way. Contact the manufacturer of your microprocessor upgrade card for support information.
If your Power Macintosh G3 or Macintosh Server G3 computer has a build-to-order (BTO) 128-Bit 2D/3D Professional Graphics Accelerator Card, see also "Mac OS X 10.0: 128-Bit 2D/3D Professional Graphics Card Causes Kernel Panic".
Additionally, the computer should have:
128 MB RAM (memory) or more for Mac OS X v10.3.9 or earlier.
At least 1.5 GB free hard disk space. Note: For Mac OS X v10.2 or later, 3.0 GB is the recommended minimum. The exact amount required depends on your computer and how you install Mac OS X (default versus custom installation, for example).
Mac OS 9.1 or later for Classic applications.
You should also read the Before You Install document included on your Mac OS X installation disc.