Generally flooring like this is laid along the longest wall. If there isn't one, it's up to you. Just make sure you measure it out beforehand so you won't end up with a last plank being 10cm or something. Same goes for the width. If you end up with the last one being a few cm, it's better to start with half a plank.
Think about what room it might carry over into. Laying it short way in a small room can look weird while it's not as noticeable in a larger room with furniture.
I'd start on the left side then work my way to the right. Slowly but surely placing each floor in parallel to the last. I'd apply the grout ever so lovingling, caressing the seem between floors. I'd fill the gaps with a mortar and pastel slowly working the tool into the floor until it is satisfied. I would say to the floor "there is no other way" as I get it wet with my mop, spraying every inch of it with thick sprays of soap. The floor would know it was wrong but love it too much to care. The floor and I would lay in a heap our bodies intertwined and pulsing in post flooring bliss.
Usually you want the long side to go against the longest wall, this is to minimize cuts. But it's really a matter of personal preference, there is no "wrong way" as long as you leave expansion room on the edges and have a way to cover any rough edges around the doors and transitions. Also from experience make the offsets between rows somewhat random, even a three row pattern can be seen.
The text in the body of your post literally says “I’d do it like this” and then your picture indicates that you’d start in the middle. You might see how I came to such a conclusion, as a result.
#1 - What direction are the floor joists running, you would typically run perpendicular to the joists to minimize waviness on the floor.
#2 - You would typically run it longways past the door, so the sun shining in doesn't go along the board length.
#3 - There's really no WRONG way to do this, because the LVP flooring doesn't have much structure to it, and it'll just follow the contouring of the subfloor. So whatever way you think looks best, go for it.
#4 - If the walls are really out of square, you can also go at a 45 degree angle to hide that. It'll use up a LOT more flooring, but it also looks pretty cool when it's all done.
edit: Picture #2 would be the more "right" way to do it, but again, if that's not what you like, then it's up to you. Also, not sure if this was just the way you are demonstrating, but you're also going to want to have a little more randomness in the board ends, don't have them alternate in a pattern like you have it.