CV(L) : Akagi, Kaga, 2 Shoukaku sisters, 2 Hiryu sisters, Jun'you, Ryujou, and 1-2 CVL in your choice
CA(V) : 4 Mogami sisters, 2 Tone sisters (If you can't afford the blueprint for Kai Ni, level up mogami sisters first), 4 Myoukou sisters, 1-2 Maya sisters (Maya is a must for AACI, include Choukai if you can afford blueprint)
CL(T) : 3 Kuma sister (Kitakami, Ooi, Kiso. Must for opening torpedo), 2 Sendai sisters (Sendai & Jintsuu), Abukuma, Isuzu (must for OASW)
DD : You must have at least10-15 DDs at your choice, but most common are : 4 Akatsuki sisters, 2 Shiratsuyu sisters (Yuudachi & Shigure), 2 Ayanami sisters (Ayanami & Ushio), 1-2 Akizuki sisters (unbuildable, drop from map/event.), Fubuki (if you don't have Akizuki sisters), Shimakaze, 2-4 Asashio sisters, Yukikaze.
I think that's all what you need for smooth run. Try to level them to at least hit Kai Ni or 50-70 if they don't have Kai Ni. For leveling you can find guide at the top menu under Tutorial. For equipment, focus on carrier planes first, then ASW equipment, then Surface Radar. Focus craft on equipment that have high stats, don't craft guns, except High-angle 10cm main gun for your DDs (or you can keep 12.7cm red gun, difference on AA stat only). And try to stockpile resources and buckets after an event got announced (typically 1 month before the event).
Well, those are what i think minimum for easy runs. There are a lot since some maps require different composition. Next is Summer event around 3-4 month away, so there's plenty of time to improve.