Q: OSX 10.4.11 to 10.5.1 or 10.6.1?

Hello, 10.5.x is as far as you can ever go on it, & 768 MB may not be enough to have speed to your liking.

Leopard requirements/10.5.x...

    *  Mac computer with an Intel, PowerPC G5, or PowerPC G4 (867MHz or faster) processor

minimum system requirements

    * 512MB of memory (I say 1.5GB for PPC at least, 2-3GB minimum for IntelMacs)

    * DVD drive for installation

    * 9GB of available disk space (I say 30GB at least)

Trouble is Apple no longer sells it, check eBay & such for the Retail version, not the Gray Discs...

http://www.ebay.com/sch/i.html?_nkw=mac+os+x+leopard+retail+10.5

For more on 10.5 requirements, read:

https://discussions.apple.com/docs/DOC-2275

Note, the bus speed is NOT the same as the processor speed.

Three machines were known as PowerMac 6,1, all were 1 Ghz or better, so you meet the Mhz requirement: http://www.everymac.com/systems/by_capability/mac-specs-by-machine-model-machine -id.html

Mac OS X 10.5 Leopard installation system requirements

http://support.apple.com/kb/TA24950

Leopard is no longer available at the Apple Store but may be available by calling Apple Phone Sales @ 1-800-MY-APPLE (1-800-692-7753).

If you can't obtain a retail install DVD from Apple, look on eBay or Google the installer part numbers to possibly find at an on-line store. Here's what to look for:

MB427Z/A  Leopard 10.5.1 install DVD

MB576Z/A  Leopard 10.5.4 install DVD

MB021Z/A  Leopard 10.5.6 install DVD (single user)

MB022Z/A  Leopard 10.5.6 install DVD (5-user family pack)

Installing Mac OS X 10.5 Leopard

http://support.apple.com/kb/HT1544

Mac OS X 10.5 Leopard Installation and Setup Guide

http://manuals.info.apple.com/en/leopard_install-setup.pdf

After you install the base 10.5, download & install the 10.5.8 combo update at http://support.apple.com/downloads/Mac_OS_X_10_5_8_Combo_Update

The DVD should look like this

Caution - Leopard does not support classic mode. So, if you currently open OS 9 apps in classic mode, you won't be able to do this if you upgrade to Leopard.

 Cheers, Tom

167 Mhz is the bus speed.  I just finished explaining you have at least 1 Ghz, because of your Model Identifier being PowerMac 6,1.  So you have sufficient for Leopard.