How to choose a sensible local domain name for a home network?

The question has been treated in detail on ServerFault. Executive summary; do not use .local or another dummy TLD, use a real domain.

dan bernstein (of qmail fame) has a site dedicated to choosing a dnsname for the local network (http://cr.yp.to/djbdns/dot-local.html):

It isn't easy to choose a safe top-level local name. The global root
operators add new top-level names every once in a while: for example,
.info was added in 2001, so people using .info as a local name were
unable to reach global .info sites. Software authors sometimes set 
aside top-level names; for example, I'm told that Mac OS 9 does something
weird with .local, so it can't access local names in .local. Here are 
some reasonable choices of top-level local names:

 .0       (good for machine-specific names)
 .1
 .2
 .3       (good for department-specific names)
 .4
 .5
 .6       (good for corporation-specific names)
 .7
 .8
 .9
 .internal

In 2018, IETF approved RFC 8375 reserving .home.arpa for use in home networks. (Although the specification is from the Homenet WG, it explicitly states that the name is meant to be usable in any home LAN and not just HNCP-managed LANs.)

(The reason for the two-level name is that .arpa is under IETF's direct control and it is enough to just have an approved RFC to create a domain under it, while the root zone is under ICANN management and creating a special TLD would involve much more bureaucracy.)