Renting a few bikes might be a good idea although it might be hard to find one that fits. I am also around your height and have bought most of my bikes by looking at geometry charts and ordering them on faith.
People always say to test ride bikes before you buy but I can never find a bike my size to try.
If you have to sit straight up a comfort bike may work, or a hardtail mountain bike. Maybe even a cheap cyclocross bike.
The challenge is going to be finding your fit/position.
Most of us have tried multiple saddles, too.