I'm a relatively recent Lightroom user so I feel and understand your pain. I'm not an expert but I have gone on some epic searches to solve some problems.
Reading what you wrote, off the top of my head, I feel like I went through some of these same issues when I was first just getting used to the concept of how to properly use LR and it's catalog system. My initial issue was that I wasn't importing new images so I would wonder why I wouldn't see them even though they were in the same folder or subfolders of images that I could see. I just thought LR would find them.
Quote: I need to know how to just "start fresh" with a new set of pictures, without adding to the set I have open right now.
Upon import to LR, depending on what method you choose to import your photos (move, copy, add, etc), it adds the images to your catalog and remembers where you told it they would be (or where you wanted it moved to). So if I understand your issue correctly, it seems you are importing images in the same folder so it shows up in LR under the same folder/set. If you don't want newly imported pictures to be in the same set or folder, either A) move the new images into a different folder then tell LR you want to import those images while keeping them in the existing location or B) upon inserting your SD card or wherever the images you just took are being held, tell LR to import them and move into a folder and location of your choice. Now in the Library tab you will see those new images and they won't be added to the other folder of images you were working on.
TLDR: Wherever you tell LR the images are or will be when you import your photos, that is where Library will find them.
Hope that helps. Once you figure out your workflow for importing and organizing your photos, everything makes more sense. The rest of it is just experimenting and seeing what others are doing. You have been given some great resources by the others here. Try not to look at it as a whole thing. It is overwhelming. Just tackle one issue at a time as you encounter it. Best of luck!