Human sexuality works roughly like this:
First of all, males find females a lot more attractive than vice-versa. Secondly, females are more choosy, have a lower sex drive, more sexual disgust and wait longer before they date (the poorer a choice the male seems to be).
Naturally, females wait for multiple males to showing interest, which encourages competition among the contending males. Females are strongly attracted to the winner of this competition, which might not even select the most physically attractive guy. First and foremost it's about dominance (source) and that also often comes down to competence (though there are diminishing returns above an IQ of ~120); but being attractive is also a major source of confidence, so attractiveness also strongly plays into this.
The winner of the competition will be able to protect the woman's choice from the contenders as he has proven to be the most dominant male, which also agrees with the so called "bodyguard hypothesis" which states that women have evolved to prefer physically stronger men because they are weaker and thus benefit from a bodyguard.
Hence, in the natural setting, there is really not all that much choice on part of the females, but, instead, the main selection effort occurs in a competition between males.
Women can, however, affect the competition by gossip and indirect aggression, so they can manipulate the hierarchy to their likings.
In unnatural situations, e.g. online dating or speed dating, women actually do choose. There was a study showing that women (and their mothers) indeed only take positive personality traits into account at and above a "moderate" level of attractiveness (link), but, generally, looks are still a somewhat stronger signal than personality, for both sexes (which has been shown by countless studies by now).