The "Mexican" food you're familiar with in upstate NY (Binghamton saying hello) is almost certainly TexMex, which is a distinct cuisine. Don't get me wrong, I love the stuff and have since I first lived in Texas nearly 40 years ago. But TexMex is a distinct cuisine, one highly influenced by northern Mexican cuisine, but built on ingredients and methods and etc. found in the southern US.
Just like with France and Italy, say, Mexico has many distinct and varied regional cuisines. If you're interested, Diana Kennedy is a good place to start your research.
I was in exactly your shoes at one time. I came back from my first trip to Mexico in love with Mexican food, which I'd never had before, and wanted to reproduce it at home. But this was in the early 70s in New Orleans, which had little or no Mexican or Mexican-American population at the time. Almost immediately I realized that what I already knew about cooking -- ingredients, techniques, etc. -- was not going to get me what I needed to produce the flavors I'd enjoyed in Mexico.
Then I came upon Diana Kennedy's book, "The Cuisines of Mexico" and not only were my eyes opened, but I had realistic hopes of creating at least some authentic dishes at home.
I believe the only way you can get a copy of this now is from a library, so do try to see if your local library has it. Don't worry if you can't get all the ingredients and stuff she mentions, just READ the book. It will ground you in how and why the textures and flavors of various dishes are achieved and also give you some background into the different regions of Mexico.
The book was re-issued as "The Essential Cuisines of Mexico", which is a compilation of three of her books, including the original Cuisines of Mexico. I'm including the Amazon listing for it here because of the "look inside" feature, which will give you an idea of the contents.
Because of your obvious desire to learn and to make real Mexican food for yourself, I urge you to start by getting your hands on this book. Seriously, it will get you going like nothing else will.
Diana Kennedy's Essential Cuisines of Mexico based on her 50+ years living and traveling across the whole country.
The Essential Cuisines of Mexico by Diana Kennedy. Compiled after 50 years of travelling throughout Mexico.
Japanese Cooking: A Simple Art is coffee table art book meets cookbook.
How is it possible in a community of chefs that no one has mentioned Diana Kennedy? Her Essential Cuisines of Mexico is the definitive work in English of regional Mexican food. She drove 800 miles from her home in Mexico to donate her collection of cookbooks to the University of Texas at San Antonio's archive of 2,000 Mexican cookbooks from 1789 to present.. When she was 96 years old. There's a great documentary about her and her research.