Hi,
The supported operating system versions can be found here:
Macintosh Performa 200:Technical Specifications
The original system mentioned is 7.0.1P.
The Classic II is basically the same machine, with a plain System 7.0.1 as the original system software:
Macintosh Classic II: Technical Specifications
A System 7.0.1 download can be found here:
http://download.info.apple.com/Apple_Support_Area/Apple_Software_Updates/English-North_American/Macintosh/System/Older_System/System_7.0.x/System_7.0.1.smi.bin
You may want to carry out a test with a plain 7.0.1 on the Performa 200. Another (working) pre-1998 Macintosh computer (preferably, running System 7.5 or higher) with a built-in floppy drive for 1.44 MB will be needed in order to make system disks from the file. An appropriate ready-to-use version (for example, 4.0.1 or 5.5) of StuffIt Expander will be needed for the MacBinary (.bin) decoding. The .smi is a self-mounting disk image. Disk Copy 4.2 (http://download.info.apple.com/Apple_Support_Area/Apple_Software_Updates/English-North_American/Macintosh/Utilities/Disk_Copy/Disk_Copy_4.2.sea.bin) will create sector-copied floppies from separate disk images (visible once the .smi has been mounted).
Most later versions were not free. There was a download from Apple of a full System 7.5.3, but it would take up much space on the hard disk, and it is going to be slower. A Network Access Disk 7.5 (http://download.info.apple.com/Apple_Support_Area/Apple_Software_Updates/English-North_American/Macintosh/Utilities/Network_Access_Disk_7.5.sea.bin) was made available for startup and networking purposes.