Before getting into the specifics around which kinds of texts you may have encountered once you were a reader, there is a need for a quick clarification. While your mother may have taught you the alphabet first as it wasn't an unknown approach, just learning the alphabet likely didn't play a big role in helping you learn to read. That is, for most the 18th and the early part of the 19th century, when children were taught the letters, there was no real connection to speak of to sounds or words. So, you may have been able to recite A, B, C, etc. but likely would have had no real understanding of what each letter looked like in different renderings or that the letter M next to the letter O next to the letter M sounded like /mɑːm/ and meant the nice lady who took care of you.

There were, though, exceptions. Although the Alphabet Song as we know it wasn't copyrighted and popularized until the 1830s, there were songs like Apple Pie ABC or more delightfully known in text form as The Tragical Death of A, Apple Pye Who was Cut in Pieces and Eat by Twenty-Five Gentlemen with whom All Little People Ought to be Very well acquainted that connected letters to some sounds and shapes.

If your mother had formal education, she may have held onto her McGuffey Readers which hit the market in 1836 and quickly became ubiquitous. The general idea behind the readers - and one of the first articulated theories of reading instruction - was that learning to read required a sequence of skill development. The thinking was that a young person needed to learn harder and harder lists of words, sound combinations, and English rules until one day, they could read anything put in front of them. The approach is generally described as "whole-part-whole." (Reading whole words, deconstructing to learn the parts, then reassembling into familiar and new words.) This was a contrast to the so-called "word method" which required students memorize lists of words to prepare for those words in texts and was just "whole." There were books available that supported both of these approaches to reading and there was no really way to be sure which one worked. It wouldn't be until well into the 20th century that educators began considering those with "disordered reading" or dyslexia and really trying to nail down the idea of how to best teach reading. To borrow from an older answer I wrote about reading in the 1920s, virtually every adult who has worked with children throughout history had a general sense of how reading works. We expose a toddler to lots of sounds and words -> help them connect the sounds they hear to the marks that represent letters -> the marks to words -> the words to things they see, hear, feel, and experience in the world -> and eh voila, you have a reader. It was the mushy stuff in the middle that we've only just (like the last 30 years or so) begun to meaningfully understand.

Instead, what's more likely to happen is you learned to read in a way that was not that dissimilar from a child from a family of means - you gained exposure to words, sounds, and letters via environmental print. For example, if your mother wanted to actively teach you to read, she would likely read you words found on household products, in periodicals she got, in letters, or books that she had. Other adults may have read texts aloud to you and pointed to words as they read, helping you learn the connection between what you saw and heard. Which is to say, it's entirely possible to learn to read without knowing the alphabet and you were likely in her lap looking at words long before you could "read." In effect, you weren't taught to read as we think about it today.

Back to your mother and texts - if it's after 1826, the odds are much higher that your mother - or a group of parents - could subscribe to a monthly magazine sent through the mail written just for you. "Juvenile literature," first coined by abolitionist, suffragist, and Indigenous rights advocate, Lydia Marie Child, was available in the form of her magazine, The Juvenile Miscellany. Although she assumed her readers were already able to read, she did include games and short stories for younger children who were just beginning to understand how language worked. (She also included some puzzles in each addition, linking reading and writing as a paired set of activities.) Although she stopped publishing in 1836 due to negative responses to her anti-slavery work, other publishers recognized the power of the juvenile market, making them readily available.

Access to juvenile literature, though, did depend on parents knowing it was an option. So, if you were in rural New England, odds were good they would have heard about it from another family or at church. Child's writing - and most of the other texts that would follow - provided a Protestant perspective but weren't necessarily scripture-based. Traits like hard working, obeying one's parents, being responsible, etc. were central. If, however, you were far from a city, you likely wouldn't see such texts and would read whatever your parents had around the house - which is to say, mostly likely The Bible. The closer, though, we get to the end of the 1800s, the more likely you would have had access to some form of a communal library that would have contained other texts, including classical texts like you mentioned.