The best grip for pull-ups, lat pulldown, bench press, shoulder press etc. is when you are at 90 degrees at the shoulder, you are at 90 degree's at the elbow. This ensures that you get full range at the shoulder, while getting limited range at the elbow.
Always remember more range of motion means more muscle stimulation
Example, we will draw three stick figures with different hand grips doing a bench press one at the beggining of the motion (with the bar just above the chest, if you want me to explain why touching the bar to your chest is bad unless you have a huge chest let me know) and one at the end of the motion.
Draw one with a narrow grip, beggining and ending something kind of like this - start <o>, end lol (sorry I had to get creative, the <> represent bent arms, the o represent the head, and the second lol represent the arms when straight with the head in the middle)
Draw another with a 90 degree at the shoulder, and 90 degree at the elbow grip, beggining and ending
Draw your last with a wide grip, beggining and ending
So the two main muscles that we will be looking at will be the chest muscles that bring your arms in towards each other, and the tricep muscles that extend the arm.
So the criteria for which muscles are being asked to a lot of the work will depend on how much the joint is moving. For the chest it will be how far your shoulder rotates (or bring the part of your arm where your biceps are (humerus) together) and for the tricep it will be how much the elbow is moving.
NOW LOOK AT YOUR DRAWINGS
So out first diagram, the close grip bench press
Tricep - You can see that you start with your elbows bent to a much greater degree, which if you extended them would cause a lot of range of motion at the elbow, because you start with your arm very bent and then straighten it all the way.
Chest - Your biceps (humerus) are coming in all the way to the midline so we know that this would not be limiting to the chest because the range of motion is there.
However like I said, more range of motion means more muscle stimulation so really your chest isn't being worked as hard as it can, and the smaller triceps are likely to give out first. So this would not be optimal for chest.
Tricep - your elbows start out at 90 degrees and then straighten, so we know your tricep is not going to be as stimulated as in the first diagram.
Chest - Your biceps (humerus) are coming in all the way to the midline so we know that this would not be limiting the chest just like the first one.
This would be ideal, your triceps are not being as stimulated but your chest is.
Tricep - your elbows start out at more than a 90 degree angle and straighten, so there is even less stimulation of these muscles than all three.
Chest - because of the wide grip your biceps (humerus) are not coming in nearly as far to the midline at the end of the movement.
So while this one looks good from a secondary muscle standpoint because it is not stimulating the triceps as much, it is not stimulating the chest as much either. This is also really hard on your shoulder.
Now you can take this and apply it to Lat pulldowns. The two joints that we will look at will be elbow and shoulder again. The bicep flexes your elbow, the lats pull the part of your arm where your biceps are (humerus) in to your sides.
Same thing - with a narrow grip your elbow is moving a lot and so is your shoulder so it would be effective at targeting the lats, but the bicep is being called to do a lot of the work too.
90 degree all around grip - your still getting great range at the shoulder, and limited range at the elbow which is putting a lot more work towards the lats.
Wide grip - even though your elbows aren't moving as much neither is your shoulder.
Some will tell you that a wide grip is good for building wider lats, but those are the same people that will tell you a preacher curl works the lower end of the bicep
Now you know the basics of biomechanics (unless I have lost anyone) as long as you know what joint the muscle moves, and how it moves it you can evaluate any exercise.