Alright then, so this is the structure that I will use.
I tell you, having never been in the military I never realized just how complex and confusing this could be!
Thank you everyone for all your answers and enlightenment!
There's a lot of historical stuff that is problematic.
The US symbol system, essentially imposed upon NATO, is US centric. Note that the number of X's is also the expected number of stars on the shoulders of the CO.
As for Traveller...
Regiments and Brigades seem to be the formational units, with Divisions, Corps, Armies, and Army-Groups (XXXXX) being essentially field formations.
Some terms for you:
Administrative Formation: a unit that exists on paper, but in practice is just a headquarters, with its various units routinely assigned under other commands.
Field Formation: a unit that is put together for a specific theater, usually comprised of multiple smaller units that are standing formations.
Standing Formation: a unit that has a full time existence. In the US Army, pre WW I, all standing units were Regiments and Companies.
Ad-Hoc formation: a formation made from a portion of a standing or field formation on an as-needed basis. In the US pre-WW I, Battalions were ad-hoc - the Colonel took the 1st 4-6 companies as 1st Battalion, the Lt Col the next 4-6 as second battalion, and the Major the last 2-4 as third battalion.
Notional Unit: a unit that is what is theoretically supposed to be. Practice varies. Widely. For example, some US Regiments have as few as 4 companies of 50 men each, but the notional Regiment is 3 Battalions of 3 companies each, the practical is anywhere from 6 to 20 companies.
Several other concepts, simplified
Unit of Enrollment: What size unit one enlists into. In the US, it was (pre 1890) the Army Regiment, then (1890-1956) the Corps (renamed Branch), then, post 1956, the service. The USMC was notionally a single regiment until the USCW, then a brigade, and the modern is actually a full sized army... Note that as it expanded, so also did the Commandant's rank. The USMC itself has always been a single unit of enrollment, unlike the Army.
Foundational Unit The notional unit size that is the defined standard level, and is used in practice.
Unit of Identity the notional unit at which the troops identify as "I'm in the Xth". Usually also the unit level at which distinctive unit heraldry exists. Air, it's usually the squadron. US army has varied from Regiment, to Battalion (3-39 Inf) to Brigade (172nd) and Division (6th ID).
Deployment Unit: the notional unit size at which units are deployed as whole bodies. Currently either Brigade Combat Teams or Regimental Combat Teams, air squadrons, and field hospitals
Tactical Maneuver Unit the smallest unit normally separated tactically within an engagement from it's CO's CO. Currently, various nations range from Squads to half-companies... in the 19th C, it was usually the company, sometimes groups of 2-4 companies, depending upon the Regiment (US) or Battalion (UK) commander. Medieval Armies, it was usually the Company...
Patrol Unit The size of unit normally sent out on patrols. In the 19th C, it was often a full company, tactically dividing into four platoons.
Band of the Hand a conceptual limit on direct control - a CO can't directly supervise more people than he has fingers. THis is why most units break into 3-5 sub-units.
Rule of 10 Most higher commands operate on rule of 1:10 Command:subcommands. Often, this is 2 levels up or down. This dates back to the Roman Republic. Often, it winds up being as many as 12-18 subunits on paper, but they group into 3-5 ad hoc subunits...