There are so many moving parts, it can feel like you can't get ahead in the game. Just keep driving forward and crashing. Eventually things will just click and you will understand the basics.
In addition to Das' excellent videos, a nice supplement is eXplorminate's "Over eXplanation: Top Tips for Starting Out in Shadow Empire."
Don't rage quit playing the game when you get into your first logistical nightmare. Or when you surround a minor's capital with your non-upgraded initial troops and can't seem to take it or starve them out. The game is totally worth getting past these and learning how to get ahead.
Keep upgrading your capital's Truck Station. Also, someone on Reddit recommended putting a Truck Station I and Supply Base I every four hexes on roads. I don't know if this is the most efficient thing possible to do, but ever since I started doing this most (not all) of my logistical problems went away.
Sometimes the best way to conquer minors is diplomatically, especially if they have a lot of troops and highly defensible terrain. If you use the diplomatic cards to eventually unify them, you get all their militia units. These are generally garbage, but can still help scout territory, help pacify other minors, and screen your main forces from majors.