I have 2 usb’s, one is 4gb and one is 1gb. I wanted an O/S small enough to run off the 1gb, I know I could easily use the 4gb to do it.
There are several live distros that can be run off of a 1GB flash drive. Basically, look at their download size and if they are 950MB or smaller then they can be copied to the flash drive and run as if they were on the optical disk -as in, the system does not try to write to the “disk”. If the distro you are looking at does not have pointers to how to do it from them, simply look at other popular distros from a similar line (Ubuntu, Debian, Red Hat -based) for specific steps, or do a search for “boot from usb drive” for more generic instructions.