As someone who spends multiple hours a week on Discourse instances, I think I can give you a workflow that may help. So the following is how I personally manage my way through a single Discourse site:
But first, some definitions and clarifications to your questions, which will help my flow make more sense.
Watched
This means you’ll be given a notification when there is a new post on the topic or a post on any topic in the category or tag that you are Watching. So, as you would expect, this has the potential to lead to a large number of notifications on a forum like this one.
A topic will automatically be set to Watched if you created the topic.
Tracking
These topics will show a number in a green bubble next to a topic like the picture below. They are topics you want to keep an eye on but you don’t want a notification on. So think of it as one step down from Watching.
This status will be automatically set if you reply to a topic or if you’ve spent more than four minutes reading through the topic. So if you have the topic open for four minutes or longer, it will trigger this for you.
Unread
These are topics that are marked as Watched or Tracking that have posts you haven’t visited yet.
New
Topics that you haven’t opened at all.
Joe’s Workflow
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I typically set my homepage to Latest. You can do that here. I do this because I like to scan the latest topics just out of curiosity. This is handy when I only have a few minutes and want to see if there’s anything quick I can respond to.
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From there I go to Unread. This lets me see the topics that are either my own topics with new replies or topics that I’ve shown an interest in by replying to them or marking them as ones I want to track. These are easily the most important to me in some way.
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My next step is New. But I only go here if I have time. It lets me see everything that I haven’t opened or visited in any way.
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Finally, I go to my Bookmarks. As I go through each of these previous lists, I will bookmark topics I want to come back to later. Think of it as a reply-later for Discourse.
Let me know if there’s a piece of this that doesn’t answer your questions. I know I didn’t address your questions directly. So be sure to follow-up with me on this. I’m Tracking. 
Last point, if you’re really really new to Discourse, I highly recommend sending a private message to @mpubot and say hi. You can interact with the bot to learn how to do things in Discourse.