Where do the older forms of Judaism fall into today’s schema? Specifically Misnagdim?

I am very curious, because my family were (Litvak) Misnagdim and Rabbinical, as well as adherents of Halacha, even for quite a while after they came to the U.S. — my great-great-grandfather brought his family to America when he was nearly 50 years old, and he was trained in the Rabbinate but did not himself pursue it. His father, however, was a Rabbi (I only know he was “Misnagdim”) as well as a Levite, not Cohain. They married into several Cohain families, although unsure if that’s relevant. Not so many were pious, but some very much so.

Okay, so what? So, his daughter was my great-grandmother, mother of my grandmother who is still living, first born in the U.S. — she initially attended Hebrew school in NYC in the 1920’s, they spoke only Yiddish at home, she complained about having to walk Manhattan on Friday evenings, they kept very kosher, her great-uncle was President (? It is in his obituary) of a Synagogue himself, and it seemed that most of their family friends were rabbis, but she came from little family, there was a lot of tragedy and early death, and she married someone who was Jewish and favored either Reform or Reconstruction (I could not tell you which). She converted and every weekend, always attended Synagogue, which I remember well as a kid.

I feel more connected now to my ancestors, through decades of research and reading their journals, learning about their lives, reaching out to cousins, than my grandma did. She actually didn’t know some of the family I do. At any rate, I just wonder:

Is there an equivalent today to Misnagdim? Her older family were from two places, from near Minsk and then Kovno, they moved due to Rabbinical appointment. Or would it just be considered “Ultra-Orthodox” or “Orthodox”? I would love to better understand this.

It is my intention to convert in time, but I do not know to what. At present, I am not even “Jewish” because my mother was born to secular/Atheistic parents who were not Jewish. Plus my father’s bar mitzvah was apparently either Reform or Reconstruction (he can’t personally remember since now, he is only culturally Jewish and does not go to Synagogue; I think he’s Buddhist now, but not sure honestly — I am not close with my parents, who live thousands of miles away from me and have little interest in Judaism. My mom, perhaps, has more, as she married a second Jew after my father who was Sephardic and Israeli, but also very secular now).

I also would like to go to a Synagogue that my ancestors might have considered? Which rules out Chabad, right? They would have been warring with Hasids, no? I have not been to Synagogue in a long time and want to go to the right one. My options where I live are Chabad, Conservative, and Reform only. If I drove further, maybe a few others in the California Bay Area.

Thanks for your insights! It’s a sensitive question, obviously. No one in my family will discuss even this much with me.