Reddit mentions of the quantum universe: everything that can happen does happen. brian cox & jeff forshaw

I personally quite like Brian Cox and Jeff Forshaw's works, Why Does E=mc^2 and The Quantum Universe which talk about relativity and quantum mechanics respectively. I found these very accessible when I was doing my A-Levels (which I think is the equivalent of American High School) and they require absolutely no knowledge of maths.

If you're more interested in Grand Unified Theories (which I assume is what you're thinking of when you talk about two forces being the same force) then the only thing that comes to mind is The Elegant Universe which I've never read personally but I have heard very good things about it. It's about String Theory which is one possible GUT theory of everything (not quite the same as a GUT, see the reply) but does cover a few other areas as well.

Another book which I've heard good things about, but again haven't read myself, is In Search Of Schrodinger's Cat which has more of a focus on quantum mechanics.

Personally I would read both of Cox and Forshaw's stuff first because they are both very short so won't take long to get through. Then you can move on to one of the others, which are both a bit longer.

If you ask nicely on /r/physics or something similar they might also be able to suggest other things you would like.

Edit: There might be a Feynman Lecture or two that interests you as well but bear in mind that these are aimed at undergrads.

Edit2: I also just did a quick google search of site:reddit.com/r/physics books which threw up some pretty good results.

Edit3: String theory n'est pas un GUT, pardon my french.

I applaud your initiative and interest in wanting to learn more about QM. The advice I'll offer is based on your "having no physics background" and only pre-calculus math. That's ok, what matters more is the desire and application to learn more. I suggest that you initially stick with popular, layperson, conceptual materials and study them diligently and then keep going onto more in-depth materials.

I cannot in good faith recommend a single book about QM. I am going to offer a variety of materials (books, articles, videos) etc that I am either familiar with myself or others whose opinions I respect have recommended, and that I believe are at an appropriate level for you. From this and the other recommendations you receive, you'll probably find that you'll develop a feel for materials that are best for you. Also, for other book ideas, I highly suggest that you go to a local library and browse through the physics section and you'll probably find some books that appeal most to you.

The ideas below are in no particular order and you can pick and choose as you see fit:

For a preparatory short Scientific American article with some important to understand history and a lookahead to the future read 100 Years of Quantum Mysteries

Several people on reddit have highly recommended this LookingGlassUniverse video series on QM

For an easily accessible popular-level intro book, I've liked and many others have recommended How to Teach Physics to Your Dog by Chad Orzel.

I highly recommend a chapter from Sean Carroll's book From Eternity to Here on QM that he makes freely available on his website here. The book is not specifically about QM but this chapter is excellent and Sean Carroll is a clear, witty, and highly respected science communicator. This chapter has good material on the quantum wave function, the Schrödinger equation, and quantum indeterminacy.

Many have recommended the book by Brian Cox and Jeff Forshaw titled The Quantum Universe. I thought chapters 2 and 3 of this book were very well done but was not as keen on the later chapters. Maybe you could find a copy at a library and see what you think.

There are also some excellent materials online. One series of lecture materials I think is very good is 21st Century Science that is at the University of Oregon website. It's an excellent self-contained series of lectures and does not require math skills. It's includes more than just QM, which I recommend that you include in your study.

A nice article: 10 Quantum Truths About Our Universe

The article What is the Physics of Nothing on the energy of the quantum vacuum or zero-point energy.

Article: How does Quantum Mechanics Allow the Sun to Shine

The following are materials I wouldn't recommend to start with, but they're really good and deserve consideration:

This wouldn't be complete without a reference to the great Richard Feynman's lecture series. Part III is specifically on Quantum Mechanics. This is a classic textbook that has been used in many high schools and colleges over the years. I don't recommend starting with this, but I include it in case it might interest you.

Another reference that I wouldn't start with but feel it's good to include it in this listing is The Quantum Physics Sequence

I like this article by theoretical physicist Matt Strasler: Quantum Fluctuations and Their Energy

If you want a conceptual look at quantum field theory, particle physicist Matthew Buckley has a good article on this that is part of a longer series on particle physics. Knowing about quantum fields is important subject matter.

If you want to read some great books on astrophysics and quantum physics, I recommend the books written by Professors Brian Cox and Jeff Forshaw: Universal and The Quantum Universe

They are brilliant books and deliberately shy away from using any complex mathematics, explaining in detail all of the maths that is used.