The Classic II actually requires 6.0.8L, a limited release version of System 6 to Pacific markets because a small group of computers was released before System was ready for the release in the international market. These machines, including the Classic II, shipped in other markets with System 7 installed. The Classic II will not boot from other versions of System 6. Both of these disk images create 1.4 MB installer disks and work only on this limited group of Macs.
System 6.0.8L - Disk 1 (System Startup)
System 6.0.8L - Disk 2 (System Additions)
While both System 6 and System 7 will fit on a floppy disk, you won't be able to tell anything in terms of performance. Running from a booted floppy disk is excruciatingly slow. I can tell you from experience, though, that System 6 is substantially faster than System 7. As JDW points out, there is no discernible difference in performance between 7.0 and 7.1, and I personally think there is much more difference between System 6 and System 7 than between 7.1 and 7.5. With 10 MB of RAM, you may well be happy with 7.5, so if you need some of its features, you may want to keep it instead of rolling back to System 6. A lot of people are surprised how many of the features we "expect" from the modern Mac OSes first appeared in System 7 (and therefore aren't in System 6!). It's not much trouble to drag the "System" file out of the system folder into the Preferences folder and rename the System Folder to something like "Backup" to allow the installer to perform a "Clean Install" (which was not explicitly an option in the installer until later versions of the Mac OS). This is handy for testing and comparing various versions without erasing the hard drive.
Also, if you're not the original owner of the Mac, no matter what OS you stay with, you may benefit in terms of speed and performance from a fresh install of the system software. I always recommend backing up and erasing the hard drive during a fresh install to ensure there is no residual fragmentation.
System 6.0.8L - Disk 1 (System Startup)
System 6.0.8L - Disk 2 (System Additions)
While both System 6 and System 7 will fit on a floppy disk, you won't be able to tell anything in terms of performance. Running from a booted floppy disk is excruciatingly slow. I can tell you from experience, though, that System 6 is substantially faster than System 7. As JDW points out, there is no discernible difference in performance between 7.0 and 7.1, and I personally think there is much more difference between System 6 and System 7 than between 7.1 and 7.5. With 10 MB of RAM, you may well be happy with 7.5, so if you need some of its features, you may want to keep it instead of rolling back to System 6. A lot of people are surprised how many of the features we "expect" from the modern Mac OSes first appeared in System 7 (and therefore aren't in System 6!). It's not much trouble to drag the "System" file out of the system folder into the Preferences folder and rename the System Folder to something like "Backup" to allow the installer to perform a "Clean Install" (which was not explicitly an option in the installer until later versions of the Mac OS). This is handy for testing and comparing various versions without erasing the hard drive.
Also, if you're not the original owner of the Mac, no matter what OS you stay with, you may benefit in terms of speed and performance from a fresh install of the system software. I always recommend backing up and erasing the hard drive during a fresh install to ensure there is no residual fragmentation.