I'm searching for an adjective that is between rare and common - e.g. something that is everyday, or ordinary, or not remarkable.
Can anyone help suggest some words I might try?
First of all, common is something everyday or ordinary.
However, if you want a word that's between rare and common on a frequency scale, I suggest occasional:
3 : encountered, occurring, appearing, or taken at irregular or infrequent intervals
// occasional visitors
// an occasional vacation
// found occasional errors
// occasional episodes of chest pain
In addition to the synonyms irregular and infrequent shown in the definition, there is also intermittent.
Another option is mundane:
From Merriam Webster:
2 : characterized by the practical, transitory, and ordinary : COMMONPLACE
// the mundane concerns of day-to-day life