If I went for 2 back-up systems, are there any external memory discs/SSD that I could plug in elsewhere in the house* and add to my network via a router without having to add any more hardwear?
You need some kind of 'server' (processor) with the disk in order to share it across your network. Assuming you don't want to attach it to another PC, I think you need to be looking for "NAS" (network attached storage) which has a basic processor combined with a disk unit (and possibly built-in wifi). Obviously this is more expensive than just a disk drive.