How much weight do men or women put on this fact? Do you think there is a difference between men and women in this question?
A lot of men would like it. A lot of women would dislike it. From experience.
I am in my mid-/end twenties (male) and never have been in a relationship. I even consider to agree to a relationship with someone I am not fully convinced of. I don't we really fit very well. But I don't know whether that's unethical to agree on a partnership then.
You mean there's a person who likes you but you don't want to start anything because you don't like her that much? Since you are or have been suicidal, it might be hard for you to connect and feel strongly about anyone or anything. Even if you will never feel anything for them, I'd say go for it. Whether it's hookup, casual or a serious relationship.
I was in a deep hole when I met my first girlfriend. Never loved her, but the relationship helped get back on track in life. I later left her. Maybe "unethical" but the world has probably given you a lot of shit so I wouldn't feel too bad about it if I were you. Take something for once instead of receiving one kick in the balls after the other from the universe.
You can even tell yourself that you "want this" even if you know that you don't. Trust me, people are not ethical in relationships AT ALL. You may not realise this since you have zero experience. Think about all the horror stories you've heard about relationships.
I don't recommend marrying or dedicating yourself too much to this person. Be with them, feel better, build your confidence (you will!) and then finally fall in love for the first time. Do it.
EDIT: also you sure start a lot of threads hehe