Min herself asked this a couple of books ago. I was actually sort of torn when I read that line. The Dragon's romantic situation is so absurd that you just have to accept it, and her realistic question jarred my suspended disbelief. Still, there's a while until our next WoT fix, so chime right in. Although the women concerned do not need description, I will run them down and tell you who I like. Whom do you prefer? Or maybe you think that there's someone else?

Min: has known Rand for two years. She's short and slender, with big dark eyes and a strong individualistic streak. She's playful, gutsy, and witty. She has a lot of confidence in herself, aided by a sharp mind. She's got a strong will, and chooses to fight the Shadow (or anyone else, if need be) despite no special training or skill. She probably has the most practical mindset out of Rand's three women.
She's willing to put herself in danger to save her own life, and the people she cares about. She has a really cool, unique, power. She's pretty in an initially-androgynous way which probably makes her extra "hot." She has a healthy attitude toward sex and her body, and puts out a lot (not a judgment, they're in love).
She displays a willingness to seek compromise or change to get what she wants (the girly-style seducation of Al Thor). This stands in odd contrast to her initial relationship with Rand, which contained so much teasing as to seem insulting. This means that she might be the type who injects some combativeness or (possibly borderline-hostility) into her relationships.
Still, she has no particular life of her own. Part of this is because she's young and hadn't found her place before getting caught up with Aes Sedai. It's also partly because she chose to stick to Rand like glue, at least as soon as she could.
I didn't like her falling for Rand because she saw it in a vision. Still, she loves him completely. She is devoted to him, to the point of placing herself in unthinkable danger. She gets extra points for having no One Power access in a world that could do far worse than kill her.
-Conclusion: She's great for Rand, and he might "choose" her. She doesn't get my vote, though.

Elayne: has known Rand for two years. She's graced with many virtues, including compassion, determination, courage, ambition, and high intelligence. She's also cheeky and given to humor, with a secret fondness for curses. She's gorgeous - tall and slender, with eyes blue enough for a Dune reference. She has like eleven names or titles.
The girl/woman is powerful too, since she's a strong channeler who will soon be Queen of one of Randland's major nations. Her love for and infatuation with Rand are strong enough to make her a little nuts sometimes. Still, she can be disturbingly touchy to the point of seeming dim - she displayed little compassion when she jumped to believe that Rand would "give her the throne."
I'm glad RJ took the time to address the fact that they're mega-distantly related. It might make for some hysterically awkward passages, but it would still be creepy, and that's not even considering the possibility of her mirror-like twins having problems.
We haven't seen her being obsessed with him, as she also maintains her own life. She has a strong obligation to her family, her country, and the White Tower. This means that she and Rand could part if the her obligations come to loggerheads. Since she'll be Queen, however, she has a many tools for resolving such a problem.
She seems to have a healthy attitude towards sex and her own body. She also has a sweet (or creepy, depending) resemblance to the woman loved by Rand's prior incarnation. Still, the basis for her connection with Rand during their courtship is that they talk and he trusts and listens to her.
Many other readers seem to find her bland, but I think they're influenced by the dreadful pace of her coronation subplot.
-Conclusion: I like her for the guy, as I loved the way they met, think she has a lot of great qualities, and think she and Rand have a lot in common; I always felt that their personalities were pretty similar. Elayne gets the "will" and "should" from me.

Aviendha: has known Rand for one year. She's passionate, motivated, brave, fierce, and honorable to a fault. Her intelligence is never bragged about nor derided, but she's knowledgeable about survival and the Aiel world. Though she has only one name, she approaches her problems with her brain. She's a tall, pretty athlete with blue-green eyes. She's busty. Bonus points for red hair, as usual.
Her personality often presents a judgmental and belittling attitude, partly because she's a hardened warrior and partly because she's out of her element in Randland. At the very least, she occasionally takes some time to think about her new surroundings and companions, making some efforts to understand them.
These things cast a nicer light on the fact that she talks like a bigot very often and has no problem with murder, possibly to the point of sociopathy (she's prolly not a psycho). Her life has been battle-driven, and that's a big factor. It's an appropriate one too, since she lives in a world that is, by definition, driven by battle. She's a little less crazy because they ARE out to get her...
She shows some potential for change in that she kindly regards Olver, a filthy little Oathbreaker who should die or commit suicide (according to her beliefs). Still, she manages to do this without actually challenging her whole anti-Cairhienen/Randland belief system, so she loses some points for that. She loves Rand, but she's the sort of girl who could kill him under the right circumstances - matters of honor that he doesn't understand, no less!
She fights hard against the Shadow. She will never give up or betray the Aiel or her friends. Of all of Rand's possible companions, she is the one who seems most capable of (a) saving Rand if he was in danger, (b) saving herself if she's in danger, (c) ripping people apart if she can't use the One Power for some reason. She not only possesses this sort of drive, and physical conditioning and fighting skill - she possesses a tactical mind that knows how to respond to crises. She is deeply-obligated to her Clan and Sept and the Wise Ones - she could be taken away from Rand over these obligations, more easily than Elayne.
It's also not clear exactly why she loves the Dragon. She's stated that she likes body and his strength in the face of his injuries. Regardless, I never liked the idea that she was told that she would love him. It seemed to start an emotional shame-spiral in which she got tricked into falling for him.
-Conclusion: I don't entirely trust her violent tendencies, or her indecipherable honor code that might result in murder at any time, even of people close to her. I don't know what the basis for the relationship is, nor recall her ever voicing why she's fascinated or in love with Al Thor.