Let's take this point by point:
The plan is to get a virus free hard drive / operating system. The way I plan to do this is to complete a system restore
System Restore is not, I repeat NOT, going to get rid of any virus infection on your computer. There is only one of two options you have to do this:
1. wipe your drive totally, including nuking the main partition. Reinstall Windows. Result: You have removed all viruses; and you will lose all data and programs, and start from scratch again.
2. go through the cleaning procedure as directed by one of the malware experts on this forum. Result is that you regain your clean OS, and all your programs and data are intact. This is the best choice.
You have no other choices. Again, you have no other choices.
Possibly the terms here are confusing you:
System Restore is a tool which is part of the Windows operating system. It will not replace Windows itself, only certain key components.
System Reinstallation deletes your current Windows installation including all programs and data, and reinstalls Windows fresh.
Backing up my current system onto my external hard drive should enable me to reinstall all the uninfected files using the macrium software, once I've restored to an earlier system point first?
No. Again, as pointed out above, System Restore will not remove any viruses, malware, adware or spyware on your computer. System Restore only restores selected corrupt, missing or damaged key system files in the event of a major system crash; it will not remove viruses.
My Post #2 hinges on getting your system cleaned of infection while still keeping your data and programs safe. I suggested making a backup first as a safety-net in case anything goes wrong; if, in the cleaning process, data is damaged or deleted, you can go back into the backup and transfer that data back on to your system. Usually data does not get infected by an infection, only the operating system itself. It is highly unlikely that will happen, the staff here go through a lengthy, in-depth training program and know what they are doing. In order to do this, however, you must have a backup program that will not just make an image, but that image must be accessible in real-time so you can access and retrieve individual files & folders. Not all backup utilities will do that. Macrium will.
At this point, my suggestion: go through the cleaning process as directed by one of the staff here. That will solve the entire problem and you will be back up and running. Then make a backup of your clean system, and start a regular schedule of backups weekly.