Having so many different models over the course of the series makes it a pain to identify when each first came into use. Most wiki entries for the ARs and BRs specify the starting year of service, others are more ambiguous. Likewise, different models appear to be standard issue for different branches:

[quote]
-The MA5B assault rifle, Marine standard issue from the 2520's until the Fall of Reach and the Battle of Installation 04.
-The MA5C assault rifle, Marine standard issue from the Battle of Earth through the end of the Human-Covenant war.
-The MA37 assault rifle, Army standard issue from 2437 through the Fall of Reach.
-The MA5K carbine, a modified variant used by SpecWar teams.
-The MA5D assault rifle, in use by 2557.[/quote]

[quote]
-The BR55 Battle Rifle is a gas-operated, magazine-fed, mid-to-long range weapon capable of semi-automatic and burst-firing modes. Prototypes of the BR55 existed as early as 2524, and were later used in 2525 during the fall of Harvest. By 2548 it had superseded the M392 Designated Marksman Rifle in use in all branches of the military with exception of the Army.

-The BR55HB SR is a select-fire rifle first fielded in 2548 as an improved variant of the BR55 Battle Rifle. The BR55HB SR was designed to further improve on the exemplary performance of its predecessor, which had seen service for over 27 years, the entire duration of the Human-Covenant War.
[/quote]
Etc. etc.

Either BR seems okay to use; I'd assume most frontline units have upgraded to the BR55HB SR. As for the ARs, it seems most plausible to be armed with the MA5B, as the Battle of Earth hasn't happened yet, and we're a Marines branch. MA5K seems likely too, being a spec ops carbine. That said, the MA2B also looks like fair game.