How do I join the IDF to gain citizenship in Israel?

I figured out my mother is Jewish pretty recently and ever since I’ve been learning all about the religion and culture. I’m almost able to understand some sentences in modern Hebrew. I’ve been reading the history of Israel and history of our people and I really want to be a part of it.

Since I didn’t grow up in shul or with a barmitzvah I consider myself an in progress convert. Right now I’m not in a position to find a local rabbi to bring me in as I’m stationed with the USAF in a place that has scarce religious resources (Bible Belt America).

I’ve got two questions:

First, what must one do to have a real conversion into Judaism in America?

Second, after conversion how do I join the IDF for a dual citizenship? I’d like to stay there for good.

EDIT: I should add; my mother doesn’t claim Judaism, but my grandmother on her side told her when she was younger that my great grandmother‘s mother was Jewish. I extrapolated from there.