of that trio, I guess I would vote for Beau Geste,
although personally I liked Reap the Wild Wind more. Campy DeMille yes, but I really enjoyed John Wayne in a bad guy turn, plus the great Technicolor.
Hayward only has supporting roles in either.
I have seen a lot of her films, and frankly most don't hang in my memory much. I Want to Live is just another of the myriad anti-death penalty lectures (I personally oppose the death penalty, but most of these sorts of films just cover the same old ground)
My personal favorite of her films is Rawhide. Don't expect it to rate very high, but I found it engrossing all the way.

I'll let you have the vote John, which of these three would you like to see at the top - Beau Geste, I'll Cry Tomorrow or I Want to Live? I'm not a big fan so I don't care, of the three I've only seen Beau Geste, it's a good film but does it represent Hayward?
There's a fraction of a point between all three.
I'll upload the video in about 8 hours.

"Susie H next, I have no idea what's at the top of her chart."
I assume this is Susan Hayward. I want to comment before I see what your list will look like. I think Hayward was an actress with Bette Davis level talent who never really got really top chances.
I imagine several of her best will be good (if not great) films in supporting rolesBeau Geste, Reap the Wild Wind, And Now Tomorrow.
Later, when her career moved into higher gear, she was in a ton of good but not great films like The Lusty Men,
and good but not great vehicles for herselfI Could Go on Singing, I'll Cry Tomorrow, and I Want to Live.
I will be very interested to see what comes out on top. I suppose I'll Cry Tomorrow or Beau Geste.

Mogambo is just a fraction of a point away from the top 5 and all the others in the bottom 5. There are about 5 or 6 films there in a tie for 5th place.
I watched Night of the Iguana years ago and can't remember if I liked it or not, probably not.
Lana and Ava both have noir classics as their chart toppers and I'm sure Babs does too. Susie H next, I have no idea what's at the top of her chart.

another star with a rather unimposing list of movies.
No argument about The Killers as #1 th111cough. By far the best film Ava appeared in.
There is a very entertaining WWII musical called Two Girls and a Sailor. As typical with MGM, lots of good musical numbers, but this is also the best of the two sisters in love with the same guy plots. Gardner has a supporting role but seems to me is on camera about as much as she was in East Side, West Side for example. I would put it in her top ten.
Night of the IguanaI recently bought a DVD of this, but haven't watched it. Am surprised at the low rating, as I have read good things about it. Still, having not watched it, I can't dispute your rating.
MogamboI think this was her most appealing performance. While not as good as the original Red Dust, I would rate it somewhat higher and certainly in her top five.