As a non-music major, I self-studied my way to become a music theory major at one of the best music theory schools in the US. It wasn't easy and I had amazing teachers who helped me along the way. There are books that I have used and would recommend others to use if they are interested in studying music theory.
Tonal Harmony Textbooks
1) The Musician's Guide to Theory and Analysis (2016)
by Jane Piper Clendinning and Elizabeth West Marvin
This is the main book I used for my self-study. It is the music theory textbook used for music majors at NYU. The authors explained the books in simple terms and used folk/pop song examples to lure music students with various interests. However, this book is rather expensive. I highly suggest you to also purchase ( or rent or borrow) the workbook that comes with this textbook.
2) Harmony and Voice Leading (any edition)
by Edward Aldwell, Carl Schachter and Allen Caldwallader
Why did I use two textbooks? I want to fully understand tonal harmony. By reading about the same concept with two different books, I get a deeper understanding of the theory. This book is the theory textbook used at Mannes. It is quite dense and can be difficult to understand. My suggestion: take make notes as you read this book. If you don't write notes, the book may be hard to follow. If you can follow this book, you will discover some of the most important and rewarding concepts about music theory.
Tonal Harmony Workbooks
1) The Musician's Guide to Theory and Analysis: Workbook (2016)
by Jane Piper Clendinning and Elizabeth West Marvin
I highly recommend this workbook that comes with the textbook I mentioned above. It has a variety of exercises: simple chord construction, figured bass realization, melody harmonization, and harmonic analysis.
Counterpoint textbook
1) Counterpoint in Composition (1989)
by Felix Salzer and Carl Schachter
This is a comprehensive, clear, and straightforward book on species counterpoint (two part and three part) and the manifestation of counterpoint in tonal music. It is surprisingly easy to understand and is super helpful. Suitable for beginners, and amazing for advanced students who wish to deepen their understanding of species counterpoint.
Score Reading Exercise Book
1) Preparatory Exercise in Score Reading
by R.O. Morris and Howard Ferguson
This book is perfect for those who have limited experience in reading clefs other than bass and treble clef. The exercises progress from simple two-part keyboard exercises involving various clefs, to string quartets or open-score chorales. I like this book because it takes time to strengthen your fundamentals in reading alto, tenor, and soprano clefs first, before introducing more clefs or voice parts.
Figured Bass Exercise
1) 371 Harmonized Chorales and 69 Chorale Melodies with Figured Bass
by Albert Riemenschneider (Editor) and J.S. Bach (Composer)
I have used other figured bass exercise books before and I think those exercises feel too artificial. The 69 chorale melodies with figured bass in this book are real melodies with common chord progressions. Hence, once you have practiced these melodies, you would have played the most idiomatic progressions in classical music. Play these exercises slowly - even if that means spending 5 min between each chord just to figure out the voice leading. Eventually, your hands will memorize certain progressions and the exercises will become easier. TIP: It is ok to let a voice drop out and have 3-voiced texture. Also, look ahead when there are suspensions.
I hope this list of recommendations help!