I think there are two different questions that are sometimes being conflated in this thread:
1- How do you determine what fit / bike geometry you need. This is based on your specific needs. There are many different ways that people figure this out: online fit calculators, professional fittings, rules of thumb based off height… whatever.
2- (what the OP asked): Once you know what fit you need, or have a bike that fits you, what are the most important frame measurements that will tell you what bikes will fit. I would say Stack and Reach. Others argue that seat-tube length (i.e., exposed seatpost) or standover height are good enough.