If I am not ancestrally Jewish...?

Does that mean I am not a chosen person, and there for cannot get salvation or become a Jew? I'm currently Roman Catholic, but I've always felt that the Jewish beliefs made a lot more sense to me- as well as the people. Would I be welcomed into the synagogue? My heritage, is that of Catholicism, (Mexican, and Russian) so I'm not really an Isrealite.