[Kenilworth]

Where you start isn't super important, no need to start on the longest wall. However, I would snap a line down the hallway to reference, making sure that wherever you choose to start, you are parallel with the hall.
It's also not worth worrying about where your side planks fall. Unless you have one square room it's usually going to be impossible to hit every wall favorably. Vinyl plank is easy to install no matter how it lays out. As long as it's square, it'll look fine.

If I were starting your job I would start in front of the patio door. This will minimize the need to work backwards at any point (which isn't a big deal but is a bit slower). Lay 3 or 4 rows to get a nice solid base, then slide it into place, square it, pop a few screws into the edge of the first row that can be removed and the holes covered by baseboard later, and rock on.

 

[Kenilworth]

Also, some vinyl plank instructions are horribly bad. Post a photo of them if you like, and maybe you can dodge some headaches.

 

[Kenilworth]

Echo the sentiment for glue down- I installed Lifeproof LVP in three houses. It's crap and I'll never use it again. T&G are fragile and the stuff scratches easily- when you end up with a scratch at some point in the middle of the field, there is no repair. With glue down, you cut out a piece and replace it. Higher quality products will come from a distributor- not a box store. Remember, too, this stuff is not a wood or tile alternative. It simply doesn't have the lifespan- it's a carpet alternative.

This is all true. Except for the board replacement comment. It's a little tedious but I've done many with flawless results.
Having a flat stable subfloor makes a big difference in the longevity of floating vinyl plank. So does your lifestyle. So does installation. As easy as the stuff is to install I've seen many guys destroy it in the process of installing. Sometimes because they followed the manufacturer's instructions.
I've installed hundreds of thousands of feet of the stuff since its explosion in popularity, and I don't love it. It can look good and last a long time, but still is a sometimes ugly, somewhat fragile product that is advertised as bombproof.

 

[Kenilworth]

Remove the protruding locking mechanism from both the long and short "groove" sides. And also a wedge off the corners of the "tongue side" locks (hard to describe in text). Have a good long flat heavy weight ready to go. And an acetone rag just in case. Run a tiny bead of super glue gel down the tongue of the boards on the floor. Install the plank and weight it immediately. Clean up any ooze. The plank is glued to those around it. Not to the floor. The only thing lost is the the mechanism that prevents your replacement board from lifting. Which the glue takes care of.

 

[Kenilworth]

Got it! Shenanigans! But smart. The super glue durable enough over time as the planks contract and expand? Anticipating call-backs at some point on the few I have out there.

I haven't heard of any failures of my plank replacements... but that doesn't mean everything. I have had a total of one job "fail" out of hundreds of vinyl plank installs. That doesn't mean they're holding up good after three or four or ten years. I'd hate to see some of the jobs I've done, where the customer wants to polish a turd and put flooring over atrocious subfloors.

But! Super glue is pretty impressive under some conditions and I suspect it holds better than the crappy mechanism on many of these floors. Wet your surfaces for an even more aggressive bond. When installing a particular lvp which is notorious for end joint separation, I have added a dot of super glue to every end seam. No news is good news I reckon.

 

[Kenilworth]

Got it! Shenanigans! But smart. The super glue durable enough over time as the planks contract and expand? Anticipating call-backs at some point on the few I have out there.

I haven't heard of any failures of my plank replacements... but that doesn't mean everything. I have had a total of one job "fail" out of hundreds of vinyl plank installs. That doesn't mean they're holding up good after three or four or ten years. I'd hate to see some of the jobs I've done, where the customer wants to polish a turd and put flooring over atrocious subfloors.

But! Super glue is pretty impressive under some conditions and I suspect it holds better than the crappy mechanism on many of these floors. Wet your surfaces for an even more aggressive bond. When installing a particular lvp which is notorious for end joint separation, I have added a dot of super glue to every end seam. No news is good news I reckon.