The most important thing is location. You want to be located where there are high concentrations of the type of women you like. More densely populated areas are best. Ideally you should also live within walking distance of places suitable for dates.
Whether you own or rent, house, apartment, or condo, most girls aren’t going to know or care. The nicer the place, the more money you’re spending on it whether you rent or own so owning is mostly irrelevant from a dating perspective. Most girls aren’t going to ask “so, do you rent or own this place?” Certainly not right away.
For single people, I feel renting is best because you never know where you’ll end up. Makes it much easier to move, or to move in with someone you’ve been dating a while with the stakes being much lower. For example, the girl I’ve been with a year now owns her own house and I own my own house too. Us moving in together will have major implications. But if one or both of us were renting, it would be no big deal - just rent a place together when ready and if things ultimately don’t work out with eachother, just go rent another place.
But if you are just trying to find out how wet it will make a girl to know that you have a mortgage on your place instead of rental payments, the answer is: not very, if at all. She will care more about the location, how nice it is, comfort, balcony, view, decor, lighting, cleanliness, that kind of thing.