Where I get confused is on how to form the four battalions into regiments and the regiments into divisions and how to account for the necessary HQ capacity and logistics. Is the "regiment" a class in and of itself that needs to be designed and filled with HQ and logistics units that I then drag the battalions into once trained?
Short answer: Yes. It is also pretty common to have the regimental formation include artillery (in the form of bombardment units, LB or MB) and assign it to 'support' one of the battalions under its control. In that case, it usually would make the most sense to have the divisional formation handle the logistics elements.
So a simple example of what your formation hierarchy could look like might be:
XX 1st Division: 1x INF+HQ105, 475x INF+LOG-S --
Set as "Use for Replacements" to resupply subordinate formations III 1st Regiment: 1x INF+HQ25, 200x INF+LB, 40x INF+LOG-S --
Supports 1st Battalion II
1st Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 2nd Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 3rd Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 4th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
III 2nd Regiment: 1x INF+HQ25, 200x INF+LB, 40x INF+LOG-S --
Supports 5th Battalion II
5th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 6th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 7th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 8th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
III 3rd Regiment: 1x INF+HQ25, 200x INF+LB, 40x INF+LOG-S --
Supports 9th Battalion II
9th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 10th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 11th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 12th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
III 4th Regiment: 1x INF+HQ25, 200x INF+LB, 40x INF+LOG-S --
Supports 13th Battalion II
13th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 14th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 15th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
II 16th Battalion: 1x INF+HQ5, 1275x INF+PWL, 75x INF+CAP, 25x INF+LOG-S
Note that to handle logistics/resupply, there are two main options. One is to use LVH+LOG units in a higher-level formation, which will automatically resupply formations under the hierarchy. The other, which I show here, is to use INF+LOG-S units with a few in each combat formation and then a large reserve held in a rear echelon formation, which does not need to be in the same hierarchy, and use the Series/Replacement mechanic to keep the combat formations in supply.
Also note that I'm not trying to show the "best" unit composition, although what I have here should work well enough, but I am only trying to illustrate how the hierarchy could look.
I've watched some of the videos out there that attempt to cover ground formations and combat, but some of the basic points that I'm stumbling on are glossed over or not covered at all. What would be most appreciated is a ground up explanation from beginning to end.
Tabled as an idea for a future mechanics EffortPost™.