We've stayed at Westin Mission Hills and like it quite a bit. Check the Starwood forum for detailed comments. I don't know the others, but from what I've seen in the literature, Marriott Desert Springs is a notch above Shadow Ridge. I don't know anything about Palm Canyon.
I would not recommend flying into LAX. The drive can be horrendous if you hit traffic - and there are many places to hit traffic. ONT is a little over an hour and a pretty easy drive, but I agree that it would be best to fly into PSP.
Again, as posted above, it is likely to be very hot.