First of all, anti-virus software to protect themselves. Without this protection, the virus can simply disable the antivirus continue to do their black deeds. Ironic.
Further, anti-virus software "hangs" on start up new files, to prevent the activation of new viruses. That is, not knowing whether there is a working virus in the system or not, antivirus prevents the interference of new viruses. And if during the scan the user will launch a new executable file, the scan will be aborted and the file is analyzed, approximately. Well, actually it's parallel tasks, but for ease of understanding, we can assume that in the same thread.
Next, anti-virus software scans your RAM, because it sits active (working) virus. After all, if a virus in an executable file, but has not yet started, it is not an active virus, it is not dangerous as long as it not run.
Well, if the RAM is nothing, then it likely is considered clean, and everything else is a matter of technology. That is, then it does not matter in which order to check. You can first removable device, then network and Vice versa. However, it is reasonable to first test the system partitions (operating system files) in case if the user wants to abort the scan early. That is, the order is not important, but it is better to start with the more critical and potentially dangerous places. And so it is a matter of each antivirus separately.