Note #1:
68030 Macs with a 16-bit data bus like the LC II, the Color Classic, and the Classic II should use no more than 7.0.1 or 7.1. System 7.5 slows these down to such an extent that they are almost unusable. System 6 is faster on 68000 Macs because the multi-switcher is built into System 7. 7.0.1 and 7.1 lack a lot of the nicer touches of 7.5 but can be built up by adding additional 7.5 Extensions (provided they work). Remember, more Extensions mean a slower system. Older 68000 Macs simply do not have the power to run System 7.5 because it adds a lot of Extensions and Control Panels, which run processes in the background. Older Macs with 4 MB or less of RAM cannot effectively run System 7.5 because it takes up nearly 4 MB of RAM. You should never use 7.6 unless you have applications that require it (Internet mostly). System 7.6 was released as a bridge between System 7.5.5 and System 8 until 8 was ready. 7.6 is basically the same as 7.5 but adds a lot more native PowerPC code. At the time of its release, Apple was phasing out the 68K Macs and working to finish System 8. Furthermore, some of your older 68K software might not work under 7.6.
Mac OS System 8
Note #2:
I would suggest using 7.5.5 on a 68040 Mac. Although 8.1 will work on a 68040, it appears to run a little slower than 7.5. Some would suggest the very opposite, but from my experience, System 8.1 feels a little sluggish on a 68040.
Mac OS System 9
Note #3:
A G3 with 256 MB of RAM or more will run OS X. A word of warning is warranted. OS X v10.1.5 runs really slow on a G3 because the Quartz graphics engine taxes the processor. Apple changed all that with the release of v10.2 Jaguar, which uses Quartz Extreme. Quartz Extreme runs graphics through the AGP chip, significantly increasing overall performance. Where before a G4 chip (or maybe two) with lots of memory was the only way to run OS X with a straight face, now you need a good AGP card. Older G3 Macs may not be able to support Quartz Extreme and thus will run rather slowly. Quartz Extreme requires 16 MB of video memory (32 MB for best performance), AGP 2x video (4x recommended), and a supported ATI or nVidia graphics subsystem.
Mac OS v10.1 (Puma)
Mac OS v10.2 (Jaguar)
Note #4:
Apple releases new Macs with the ability to run the most current version of Mac OS. For example, X v10.2.7 (Jaguar) was the most current version of Mac OS available when the Power Macintosh G5 1.6 GHz first sold in 2003. Subsequent G5 towers shipped with the ability to run Mac OS beginning with X v10.3 (Panther). See Apple Profile Specs to determine which version of Mac OS originally shipped with your Macintosh.