Two Schools of Thought when Hand Sanding - Straight-lines or Crosshatch Pattern

There's two schools of thought on the correct method or best method on which direction to move your hand and backing pad when hand-sanding.

Straight-line School of Thought
This method means to to sand in only one direction with all sanding steps. The perceived benefit is it will keep all your sanding marks in the same direction. Then, if you want to take this thought deeper this would mean if you don't get all your sanding marks out of the paint then at least they're all running in the same direction and my guess is most people will think this won't look as bad as sanding marks left in the paint that are in a crosshatch pattern and to some level straight-line scratches might be less noticeable and less unsightly than crosshatch scratches.
Crosshatch School of Thought
This method means that with each change in grit size of sanding or finishing papers, you sand in a different direction 90 degrees away from the previous direction. The goal is as you move to a higher grit paper you completely sand-out all the previous sanding marks that were running in the 90 degree angle opposite from the direction you're sanding with in subsequent steps.

Now assuming you sand all the previous sanding marks out you would then only be left with sanding marks running in one direction. If you don't remove all the sanding marks from previous sanding steps you'll have a crosshatch pattern of sanding scratches in the paint of varying depths. At this point you can either re-sand and try to remove the 90 degree sanding marks or move on to the compounding step and try to remove all the sanding marks with a rotary buffer. If you don't remove all the sanding marks using a rotary buffer then you'll be left with a crosshatch pattern of sanding marks in the paint and these will tend to be easier to see than sanding marks all running in one direction.
Sanding in Circles
Don't sand in circles. Circular motions work great for spreading out of coat of wax over a painted panel but don't work well for sanding on car paint. One reason for this is because the idea behind sanding paint in the first place is to remove some type of defect, a lot of times this will be orange peel or some type of damage that caused deeper scratches or etchings. Whatever the defect is, the goal is still the same and that is to only remove as little paint as necessary to remove the defect so you leave the most amount of paint on the car so it will last over the service life of the car.

Now follow me on this...
When you sand in a repeatable pattern, for example straight-lines, you have some measure of control over the pattern of sanding marks you're putting into the paint and also the number of strokes and thus the amount of material being removed. If you sand in random, overlapping circles you have realistically no control over your sanding mark pattern and little or no way of gaging how much paint you're removing while you're sanding. Wet-sanding paint is already difficult and risky, there's no good reason to make it more difficult or more risky so I'm not going to recommend sanding in circular motions and common sense dictates to also avoid sanding in circles.
Big Picture
Of course the big picture goal is no matter how you sand the paint, in the end you remove ALL sanding marks and then there isn't any issue with which method you used. This is easier said than done and paint hardness is a crucial factor as to how easy or difficult it will be to buff out the sanding marks and film-build or paint thickness will be the limiting factor as to how much paint you can remove with both the sanding and the buffing process. (So be careful).


Personal Preference
Because in my life I've met seasoned Professionals that are proponents of both methods, choosing the best method becomes a personal preference. As long a there's enough paint or film-build on the car to work with then theoretically, both methods will work.

Ultimate Goal - Leave the most paint on the car
The most important part of any hand sanding project is to use the highest quality finishing papers you can obtain as this will reduce the potential for uneven sanding marks while leaving the most amount of paint on the car and making the removal process faster and easier.

Machine Sanding
And in this writer/detailer's opinion, generally speaking, machine sanding is a better option than hand sanding as it will leave more uniform sanding marks that will be a lot easier to remove and the machine compounding process will always be faster and easier versus trying to remove hand sanding marks.