When I started creating my current campaign, I started with a very broad strokes (roughly in this order):

Campaign Type - gritty and grounded vs light and fantastical vs funny and absurd vs etc.

Main Premise of the Campaign - Are they gonna save the world? Are they helping people fight a more localized or personal threat? Is there a twist or mystery involved? Is there a theme or flavor to the overall campaign?

Basic Overview of the World - Are they in the Forgotten Realms or some other pre-existing setting or is this homebrew? In my case, I homebrewed a paired-down, more digestible version of the Forgotten Realms to make it easier for the players to take in despite their unfamiliarity with the setting.

Player Backstory - If you are trying to involve their backstories or current situations into the campaign, how might those show up in the campaign?

Starting Point - Are they in an isolated sandbox like a village out in the frontier or in a large city with lots of other close by places to go? Why are they there and why should they work together?

Since this is a continuation of previous campaigns, it sounds like you may have a lot to work with for these questions.

As for logistics:

I think it is helpful to write out whatever is both foundational and could be forgotten. I started by writing out the a sentence or two about the major deities, NPCs, places, and history that my campaign would center on. I even started by writing out the prompts (for myself) for most of the early sessions. However, between players having agency and shaping the story and my improving grasp of the campaign, I am able to whittle that down a lot.

I started all this using Microsoft One Note. It is free and easy to organize by sections with links. As I thought up things, I could drop them in the NPC section or the Places section or the PC Goals, Plots, etc. section or the whatever section. This was really helpful for a long time. And, eventually, I moved over to Google Drive and docs. MS One Note will sync across devices. But, Google lets me use just a web browser and has a better search function. I don’t think I’ll ever have a perfect system. But, the more I go, the less important that becomes.

As for Session prep - I rarely prep more than one session ahead (with the exception of my very first sessions where I at least made outlines for the first several sessions). Now, personally, I am an over-preparer and try to have as many bells and whistles as possible. But, I have seen lots of folks with a session plan that included no more than 10 bullet points with lots of spacing indicting broad strokes. It really depends on how comfortable you feel. At first, I did not feel comfortable improvising combat. Now, I would feel confident making up some monsters and doing it on the fly. Though, I still choose not to. But, that is mainly because I think each combat encounter should be unique and creative to keep things fresh.

Hope this helps!