(The above rendering comes from the RJPS translation, an adaptation of the NJPS translation. Before accounting for this rendering, I will analyze the plain sense of the Hebrew term containing אִישׁ, by employing a situation-oriented construal as outlined in this introduction, pp. 11–16.)
Here, as usual, אִישׁ marks the referent as essential for grasping the situation in question. This default meaning is salient because the practice of monomachia (that is, representative two-party combat) was well known to the ancient audience—and thus would have been readily recognized in this episode. (The representational aspect of this practice, with the larger army as the beneficiary, is expressed by לָכֶם.) Each of the fighters is an אִישׁ with respect to the situation that Goliath proposes.
On the presupposed cultural background, see Philip Esler’s 2012 article “Ancient Mediterranean Monomachia in the Light of Cultural Anthropology: The Case of David and Goliath.”
As for rendering into English, the NJPS ‘Choose one of your men’ appears to construe אִישׁ as a relational noun—defined relative to the Israelite army, rather than to the depicted situation. (NJPS similarly casts לָכֶם as indicating group membership.) Although it is not uncommon to render אִישׁ with a relational noun (see my comment at Josh 10:24), in this instance a situating noun is available, which would seem to be a better fit.
The revised rendering follows REB; by convention in English, a possessive pronoun expresses benefit and representation; and in a competitive or conflict situation like this, man retains its classic function as a situating noun.