Oh man there are so many starting points! If I understand the goals you gave us, they are:
Want good coffee
No pour over
Willing to do French Press
Minimize grounds in the brew
Single serve
Brother-in-law is too intense about it for my current state
With that I would recommend an AeroPress. It is great for single serving, it extracts using immersion first (similar to French Press) then pressure, the paper filter ensures it will be a clean cup (no grounds), it is much easier to clean up than a French Press, and there a lot of different recipes to play with should you ever choose to. Plus it’s relatively cheap.
Cold brew is also nice, especially when made in batches. You can probably already do this with vessels you have at home. Toddy cold brew is a well-known system. I also have (and prefer) the Oxo cold brew system - I find it easier to handle and looks better on the counter.
If you are willing to get a burr grinder you will immediately make better coffee, regardless of the method you choose! There are many directions to go here, so you will need to research to find what makes most sense to you. Skip the blade grinder. Conical burr is fine for what you’re getting into. A safe bet that will work fine for French Press, AeroPress, and/or Cold Brew is the Oxo Brew Conical Burr Grinder that you can find for around $100 in the US.
There are so many deep rabbit holes from there. Maybe you’ll come join us someday…it’s a lot of fun and one of my favorite hobbies! Sounds like your brother-in-law is lost somewhere down here too. We all started asking the same questions as you!