These are really two separate questions: accessing files on multiple computers; and, backing up computers. Your topic is about backups.
I suggest you buy two separate backup drives - one for each computer. Drive capacity should be at least twice the capacity of the computer's drive if you were to use Time Machine. Otherwise, they should at least be equal to the computer's drive size. They would be in external enclosures that support USB connections. I'm partial to the Mercury models sold by OWC. I would avoid online services because they are costly for backing up good size hard drives.
Accessing files on both computers requires you have a home network to which both computers can be connected either by Ethernet or using Wi-Fi. It's done using File Sharing. Mac Basics- File Sharing.