Is using a live cd a good idea? Will it keep the rest of my computer including storage and installed OS safe?
You are right to be cautious.
Android malware cannot directly run on a Windows PC. Android malware CAN be used as a dropper for Windows malware, however, and this is why you should be careful about hooking up your phone. But there is one method of restore that should be safe:
Boot your phone into Fastboot mode (sometimes called 'bootloader' mode) and use the fastboot command on your PC to either:
a) Flash your new image directly (usually only works for OEM images)
b) Flash or tempboot TWRP and use that to wipe your phone COMPLETELY (remove /system, /data, cache, Dalvik cache, the works) and transfer and install your new image. (usually works for custom ROMs). You can use ADB safely here as well.
Even root-access malware cannot mess with fastboot, and by extension a booted-from-fastboot recovery partition, so you should be safe restoring your phone like this.