I've had success finding good housing options in a few different environments.
My advice would be first to utilize your network. I'm not sure if there are specific channels you'd need to go through to maximize whatever housing benefits are available to you, or if they just give you a set amount of money to be used for housing expenses. But if you can't afford to live alone in a studio or 1 bedroom, it's always nicer to live with someone you know as opposed to strangers. Make a post on Facebook and see if anyone else is looking. Encourage them to share your post with their friends. Even friends of friends are better than strangers.
If you do end up looking for roommates, be as open and honest about who you are and what you're looking for as you're comfortable being. When my roommate and I were looking to rent out our third bedroom, we were up front about the fact that I'm trans, that we have a rambunctious dog, that we're gun owners, and that we don't tolerate any kind of substance use. Sure, it cut down on the number of people who were open to renting with us, but it saved us a lot of trouble in screening out people who wouldn't have ever been a good fit for our lifestyle.
As far as finding a place, look at the Trans Housing Network on Tumblr. People can post looking for space or if they have space available. If I was looking, that would be the first place I'd make a post on.
Apartment complexes will often post ads on Facebook when they're having move-in specials. I got 3 months free rent at my first apartment because I saw the ad on Craigslist while I was scrolling. It saved me $2100. Don't move into a place just because they have a good special, but definitely look and see what options are available. If you like the place AND it'll save you money, great.
Probably the best housing deal I ever got was while I was in school. My university had year-round resident advisors because they hosted a lot of summer conferences, so I was able to get hired the summer after my freshman year and I never had to pay for housing or move back home for the next three years. I don't know if you're open to going to school, but that is a pretty good way to get decent housing.