Introduction to Chemistry Textbook - Theory based
Chemistry by Zumdahl is very good. I teach General Chemistry I and this is the book we use. I still reference it frequently. You will want the instructor solutions to accompany it. I let students check this out for classroom use, but you should have it for yourself at least. (I saw for the first time this semester a version that is loose leaf; this is great since it is sort of big. We have a custom version that takes out parts not covered. There is also a nice ebook.) This book is lovely, except for electron affinity. 
For introductory chemistry, Zumdahl and DeCoste wrote Introductory Chemistry: A Foundation. We use this for Chem 101. Also very good, but a little too elementary for my taste and there is not as many topics discussed. But this may be what you want. You are probably somewhere between these two. 




The next two are probably more rigorous than you would like, but worth mentioning. 


Principles of Instrumental Analysis by Douglas A. Skoog is outstanding, but probabbly more advanced than you would like.
Physical Chemistry - Atkins. This book is very dense and is definitly rigorous. This will take an undergrad 2-3 semesters to get through. This may be a little overkill. You will actually see many general chemistry textbooks take exercises from this book. Really need the solutions bad for this book, it is that hard. A great place to find exam questions.