I'm porting into SFHA at the moment. Here's my experience after 5 years of being a Housing Choice Voucher holder.
I bring the voucher up when it is first necessary. For example: I've setup and viewed an apartment. During the viewing I decide that I like the apartment. The leasing agent is happy to accept my application. During our talk about fees and deposits and what have you I ask about money coming in from a third party. Something like, "How can a third party pay for my deposit with the least possible amount of confusion?" This is a good way to bring up the voucher and being poor.
My outlook is if someone doesn't want me there after we have met and gotten to know one another through the time it took to tour the apartment, I don't want to be there either. I want to be somewhere I fit.
I initially used my voucher in a spot that was easy to get into since I had no rental history, and a low paying job at the time. Solid way to easily secure a place to live, but if I could do it again I would take the time and effort to move into a spot that had more of what I wanted in an apartment, and neighborhood.
Good luck to you. Hope you find an awesome place, if you have not already.