LB: ZD is right. The Rabbanut only accepts Orthodox conversions, and generally only ones from a certain list.
Litvos: Welcome to the Coffee Room, and I wish you success with your spiritual journey, wherever it leads you. Gerus is often a long process and can be very difficult. Have faith that if it is indeed the right thing for you to convert, Hashem will allow it to happen at the right time. Of course, your own efforts and determination will also make a big difference.
It’s true that some gerim or their children experience discrimination or lack of acceptance, but this doesn’t happen to everyone and depends very much on the community. I personally know gerim who have never experienced discrimination after converting. Gerim often (not always) end up marrying other gerim or Baalei Teshuvah but this is to be expected, as they tend to have more in common.