Those are 2 different looks.
1st is more dressed up.
2nd is more chilled.
They both look good in terms of buttoning down.
This question made me laugh, lol!
There really is no answer to this question.
If you feel the need to unbutton then sure...unbutton has many has you like.
If not, button it all the way baby!
Having just left a job in menswear, I feel compelled to comment.
First of all, in reference to the second link, don't...ever...wear pants like that. E...ver!
Secondly, when wearing a casual shirt like that, you should only unbutton the top button. Depending on the shirt, the environment, the event, etc., you could get away with doing the top two buttons, but I usually only do the top.
Two different styles.
But for the second one it would depend if you have a built chest. The more built your pecs are, the more you can unbutton down. Sometimes you would see men with 6 packs who unbutton down all the way.
BUT USUALLY..it should be no more than 2 unbuttoned. Especially if you're wearing an undershirt.
One button undone with sleeves rolled up is what I always do. I like the collar spread like the V you're talking about, not like the squareness of the first picture
all of them can be buttoned but leave the top one. If you have a tie on, all of them should be buttoned