When to use 'ourselves' vs. 'our self'
Solution 1:
Those ones are identical with use.
Used reflexively as the direct or indirect object of a verb or the object of a preposition: We bought ourselves an espresso machine
While "our self" is non-standard, it is used when we is semantically singular as in the royal we, the editorial we, and the nurse's we, e.g. "We seem a bit displeased with ourself, don't we?"
Solution 2:
The OED contains a long entry for ourself. It has citations up through not just the 1990s but even from the 2000s. The last one is:
- 2002 ‘B. Hooks’ Communion vii. 104 The one person who will never leave us, whom we will never lose, is ourself.
It also comments that:
Originally only used for emphasis, but now in general use, replacing the reflexive us, which is now only regional (see us pron.³).
The reflexive force may be only contextually implied, and sometimes approximates to a collocation of the possessive our and self.
Solution 3:
Some dialects lack such forms as ourself, themself, that is, reflexives combining plural pronoun with singular self, rather than plural selves. As a matter of style, it is preferable, where possible, to go with forms acceptable to all readers.
It isn’t always trivial to do so, however. The self-form is obligatory for me in the following types of context (where there is a single event of hitting):
Only one of us hit ourself/*ourselves.
Only one of us hit themself/??themselves.
So, if writing inclusively, I would circumlocute here, rather than choose between a pronoun that is nonexistent in some dialects or sentence that is ungrammatical in mine.
Solution 4:
I would argue that "ourselves" is the more appropriate expression because it matches the subject of the sentence, "we". While @DavidFormas is correct in pointing out that there are circumstances in which the use of the singular would be grammatical, I suggest that the sentence flows more naturally when one does not mix a plural pronoun with a singular noun.
Solution 5:
"Selves" would be the normally correct usage. If you changed the "we" into a singular pronoun (ie everyone) you could use self, but the we and our are plural pronouns.
By the way, the way you indicated our and self as separate words is somewhat irregular. Using our or your self in this way normally emphasizes that the self is representative of the ego or essential being of the person rather than the "yourself" being simply a pronoun. In this case it follows the same rules as most nouns with possessive pronouns. As both two words and as a single word (yourself instead of your self) the plural our would still make it "selves." The only times it would be ourself is with a royal or editorial we.