Correct me if I'm wrong on this bit - the LCII came out before the end of System 6, so is can boot System 6. With that said, when the Performas came out, they came out after System 7 came out, and thus all have some form of System 7 on them. I remember that from a NYMUG Meeting as to how to increase the membership from the new Apple owners as some department stores would not allow outside advertisement on their products.
Since the software was already preinstalled, there were no floppy back ups. That was a major complaint of the systems, especially where some early hard drives failed and there was no way to recover what was there or install a new system. Eventually somebody created a freeware/shareware program to back up the system onto 25 floppies. 100 floppies more or less backed up the whole software library of the hard drive, not your data. This back up was bootable only on the first disk and ran a program to extract the rest. It also was able to create an emergency boot floppy.
As I remember, the software on the system was:
The System 7 Software (kinda obvious)
Games: Eric Solitare, Spectra VR, a couple of others. Some came with KidPix.
Utilities: QuickTime, Stuffit Expander
Office software: Last versions of MacWrite/MacPaint. Later versions came Microsoft Word. Hypercard was added later on.
Graphics: MacPaint, KidPix and in later cases PhotoShop LE (Limited Edition). This version of Photoshop was 4.0 I believed, dumbed down to be more like MacPaint and could not use PS Extensions.
If sold with a modem which some later 400/410 and most of the 420s (LCIIIs) and beyond were sold with, Communications Software: Some kind of Telnet program; AOL's software, and as the internet started- Mosaic and Netscape on later versions with membership programs to join AT&T, Genie, Prodigy, and a couple of other ISPs.
There was also a presentation cartoon movie about the Performa.
And I think that was it.