In addition to the supplies, a stack with a Supply Unit that has supplies gets a 10% boost to fire combat. So a large stack should always have a supplied SU. A large stack away from your supply lines may need several SUs to remain out of trouble. A depot must be within range (3-5 regions) of a continuous line of depots reaching to a supply source, or it won't get resupplied. A depot deep in enemy territory may not fulfill this requirement. In military jargon, a raid is for quick in and quick out operations, so a SU may slow down a small force. If you mean to deliberately take an objective deep in enemy territory, then you will definitely need lots of SUs and a line of defended depots.
Charles' videos are one of the pillars of the game's learning process. You are on the right track watching these. Divisions are the backbone of your Army structure once they become available. A Division should have one sharpshooter to increase intiative (+1). Line infantry are better than militia/volunteers or conscripts, so use as many as you can scrape together. A couple cavalry aid in pursuit/screening. If you want to make an elite Division with extra cohesion, then add one high cohesion brigade/regiment. Depending on the mission you have planned for the Division, use either intrinsic artillery support or stack the Division in a Corps/Army with an artillery Division. A Marine/Sailor aids in amphibious assault or river crossings. Good luck!
I'm the 51st shade of gray. Eat, pray, Charge!