You need to define "when choosing a mate". As you wrote it I would take it to mean "when choosing a man to have children with" which is very different than choosing a boyfriend, dating, or getting picked up.
For literally choosing a man to have kids with its money, but not just cash: stable long term job that pays enough to raise a family. Once that is ticked then it's height, status, stability, and a general "has his shit together"assessment.
HOWEVER, and this is a big however: women hardly ever make a decision like that. In most cases they end up falling into a situation with a guy they got together with for some other reason. A one night thing turns into a relationship, or whatever. This is likely hour 80% of relationships get going.
That said, I have met women online dating who WERE actively evaluating for "suitable father". Years ago I dated one girl, only maybe went out three times. After she ticked off the box that I had a good enough job and presumably that my height/status were good, her next biggest concern was whether I could cook--she was literally evaluating whether I could make meals for the kids on days she wasn't able to. She suggested we take a cooking class together.
This was in the third date. There was no fourth date... But that idea was definitely in her head.