Note all info below is based off of Caius Flavian posts here - http://starwarsrp.net/topic/87185-army-of-the-republic/
with added OCC recommendations.
Republic Army Squad - The Republic Army's smallest unit is the squad. It consists of 10 troopers led by a Sergeant. This unit also normally had up to two specialist, a medic, assault trooper, and / or engineer. This unit size is popular for those who want to play and an individual soldier and is often the basis for many special forces units.
Platoon - A platoon consists of three squads and is lead by a Lieutenant. Slightly larger than a squad as it is made up of multiples of them and is a good starting point for someone who wants to play as an officer without going to a full blown company.
Company - A company consists of in between 3 to 5 platoons and is lead by a Captain or a Major depending on the size and age of the unit. This is by far the most recommended army unit to build for newer players who want to begin to command a larger seized unit. It is small enough not to become over whelming while large enough to begin to design unit insignia, specializations and other back story.
Battalion - A battalion ranges from 4 to 8 Companies and is lead by a Lieutenant colonel. This is a good unit for those who have a well developed company and wish to grow it into a larger more complex fighting force.
Brigade - The Brigade holds a number of battalions, in between 4 to 9 and from the army capable of large scale operations, most often charged with protecting a section of a planet or other vital point of interest. With their own headquarters based on their main planet these are army units that can be deployed for large scale operations such as invading an enemy planet. The brigade is lead by a Colonel or a General depending on the size of the brigade. Your finally in the big leagues with these units, when deployed this sized unit has a massive affect on battle story and outcomes.
Division - Commanded by a General! Made up of a minimum of two brigades and can very well go up to six! Used for operations that can span a whole continent or planet! An even bigger player that takes a lot of time and effort to flesh out and build.
Corp - An army corp is a large military formation made up of a number smaller units is brought together under the command of a Marshal. An Army corp can be as small as 2 Divisions brigades and as massive as four divisions depending on its role and purpose. Corps are used to defend or attack a whole planet or even a system! Close to the whole enchilada here, these are end game units constructed by master fluff alchemists. Senate approval will be needed to get this unit recognized as canon within the faction.
Sector Army - Sector army is made of up several Corp or more and is brought together under command of a Grand General and may span multiple planets or systems even akin to the old System/Sector armies of before. These are usually created by high ranking faction officials for major operations by taking multiple smaller units and combining them.