Philosopher- I posted before your post came up, so when I wrote I had not seen your correction about Dovid.
I would call Avraham the first Jew (and not in the sense of a Yisroel today), not the first Ger. I guess that is semantics, but I don’t think Avraham Avinu can be used as proof that geirim are good. There are many famous actual geirim that could better serve your cause- Rus, Onkeles, Shmaya and Avtalyon, R Akiva’s father…