Apple TV Memory

Not entirely sure what you mean by "How much memory would an average household need to have" .

Households don't generally have memory at all.

As to memory on an Apple TV, memory is used to run apps and do the normal operations like on any other computer system. There is no memory specification on an Apple Tv directly. In other words Apple does not disclose the amount of memory in an Apple TV.

The newer 4th gen Apple TVs and Apple Tv 4K specify storage space, which is different from memory. The storage space is used to store Apps, and their data. It cannot be used to directly store media like movies or music.

Only you can tell how much storage space you may need. Rule of thumb is to go for as much as possible given your budget.

Older Apple TVs (2nd and 3rd gen) have no storage space.

Generally 32GB should be fine, unless you plan on downloading lots of Apps and games.