I have the UN46ES6150, the Sam's Club version. Here's what I ended up with using the AVS709 test patterns.
My set did exhibit some pink coloration when looking at the test patterns if the white level was too high. According to this link some sets do this. Turning the Contrast down to 75 seemed to fix that.
I used Standard Mode and Warm1 because Warm2 looked too warm for my preference.
Brightness at the default 45 seemed correct as did the default 50/50 Tint.
I set the Color at 35 using the RGB > Blue & one of the color test patterns.
I did the 2 point white balance using a 20% gray screen to adjust the R/G/B Offsets and an 80% gray screen to adjust the R/G/B/ Gains. This was done by eye while trying to get the gray test images to look gray. I ended up with:
R-Offset = 22, G-Offset = 20, B-Offset = 25
R-Gain = 15, G-Gain = 25, B-Gain = 25
I think initially the Backlight was at 12 but I’ve varied this & usually somewhere between 8 and 12 works for me. I’m pretty much satisfied the way this worked out & skin tones seem good.