[Epistemic status: not really an expert, but I can tell you what I think I know. Also, as a heterosexual male human person with some skill at introspection, I'm sure I have some insights about how men think, but I may have trouble separating that from my own idiosyncrasies.]
Evolutionary psychology tells us that human instincts are optimized for the Stone Age. The period of written history is too short to have contributed much (although there have been some small effects noted in other areas) and the modern era (however you define that) is even shorter.
Those with the appropriate drives who more successfully survived and reproduced contributed to our shared genetic heritage, while those who failed to do that were not your ancestors. Keep that in mind, and the rest will make more sense.
Humans are adaptation executors, not fitness maximizers; the instincts only had to make sense in the Stone Age and may have lost their purpose now.
Beyond instincts, culture and shared experience have a powerful influence on human minds, and this can bend some of the rules. (And, of course, individual human beings can vary a lot.) Culture evolves significantly faster than human genes but still has some inertia. Sexual mores many still cling to evolved in a time before paternity tests, when syphilis ran rampant in the cities, and contraception was unreliable. Under those circumstances, virginity and fidelity were highly valued, and this was perfectly sensible. Even absent social pressures, ignoring the traditional advice may well ruin one's life.
There are important differences in reproductive strategy, between men and women. Men need only pass on a little sperm for their genes to make it to the next generation. Their chances improve if they can contribute resources to their children, but there was a very real risk of supporting the wrong kid in the age before paternity tests. Men instinctively value fidelity and get insanely jealous when they don't have it, and (of course) are very much motivated to cheat. (A woman, on the other hand, knows if the kid is hers, and doesn't instinctively care as much about where the resources come from.) Having kids in tow already lowers a woman's value for similar reasons, because they'll take resources, and they're not his, although a his/hers/ours arrangement can still work if he's got some already. Not totally a dealbreaker for everyone. Sex is not simply for fertilization in humans. It also tends to keep the man around for long enough to help raise the kids.
Women are mainly attracted to (the appearance of) social status, as this translates to resources. Men are mainly attracted to (the appearance of) fertility. A slender waist means she's not already pregnant. Clear skin and long, shiny hair are signs of health. A healthy amount of body fat is not unattractive. Scars aren't genetic, so they're usually not a turn-off, even if it's on your face (provided the other signs are still recognizable), although pock marks are a sign of disease, and therefore a different story. Age can be a dealbreaker, because women have a fertility expiration date (menopause). There are probably many other subtle signs. Older men, on the other hand, remain fertile and may have more resources/status. So older women are competing with younger women even for the older men.
So yes, looks matter. A lot. And men probably care about it more than women do, because their instinct is to look for (the appearance of) fertility. But looks are not the whole story. Once you've met the man's threshold--you look to be fertile, in reasonably good health and appear to have reasonably good genes (usually, if the man estimates you're at least as pretty as he is), then the man is at least a little bit interested, on an instinctive level. Looks beyond that level are bonus points, sure, but other traits start to matter more. You may have competition, ultimately decided on other factors, but you have a chance. If you don't meet the threshold, then sorry, no matter how nice your personality, you'll probably never be more than friends.
There are details and subtleties, and probably signs of fertility that aren't purely visual. You can't look too much like his sister, for example. Visual signs are easier to judge in person than from a photograph; it's totally possible that a man who would skip your profile photo would be attracted to you in person, and vice versa. There's some evidence that natural body odors can convey information about immune system genes.
Either "opposites attract" or "birds of a feather" are too simplistic. Men tend to be attracted to women who share their strengths and may be more forgiving of weaknesses they don't share. They don't want more of their own problems. Again, this makes sense when you consider genes.
I feel like that's just basic background and this comment is already getting long. If you have more specific questions, I might have more to say.
You mentioned a "market value", implying a marketplace. Supply and demand matter, and different markets have different characteristics. You may be more competitive if you find the right one. E.g. women tend to be more submissive, sexually, so a more dominant woman is more valued by submissive men, because they're even more of rarity than submissive men are. (Not my kink.) Find your niche.
If you've met his threshold, a man will be much more interested in you if he thinks you're interested in him. The move obvious you can make it, the better. You can probably exaggerate this to an obsessive/unhealthy degree and he'll be that much more into you, at least at the level of instinct. (If you haven't met his threshold, he'll find this pretty annoying, and/or scary.) Remember, fidelity matters a lot to male instinct, so this would need to be exclusive interest. If you're like that with everyone, it would leave a very different impression.