I'm planning this install and just can't decide which spot is the best place to start. Any input would be greatly appreciated. BTW this is my first diagonal install.

For me, I would go with #3, assuming the two walls are outside walls. I will always figure my layout off outside walls for straightness.

Number 2 because you will have to go backwards and wrap around that wall with #1 or #3. Then you can go both directions.

The bottom wall is not a wall near 3, its a bi-level home and that is where the railing is looking down to the den.

In that case I would go with #2. I would chalk lines and check the common wall at the Dining Room for straightness with other areas. Then make any adjustments, to mark my points for a true 45 degrees. You may want to install the 1st section without wrapping the island wall. Or if you prefer to wrap that wall in the 1st section, dry lay it first.

At first I was thinking 3, but 2 makes the best sense now that I think about it.

So going with number 2 would going up towards the kitchen be the best direction to go, then backfill around the island wall and into the dining room? I think my biggest concern is going around that island wall and having it meet up around the other side of the wall closest the closet.

That's what I would do, head toward the kitchen first. Then wrap the wall & into Dining Room.

If you dry lay the planks around the island wall, it shouldn't be a problem. It's a narrow island, and as long as your cuts dont gap the field, it will go right in.

Great, thanks Howard.

Would moving line 2 back a little allow you to hit that stair nose? If so, I would do that because you want those angled cuts matching up nicely with the steps and the guardrail nosing. You can fudge diagonals being square against walls and never be seen, but open nosings / landing treads are a different matter.

Jerry I might be able to hit the landing on the right side of the stairs, I'm really not sure if that line will flow to the stairs or if its closer to the closet.

I'm not exactly sure what you mean by hitting the nosing square, to me the diagonal will be the same angle throught the house so when I do hit the noising it should be fine?? I have seen this mentioned before, but I don't quite understand.

You say this is a split foyer home with a guardrail on one side of the stairs? Normally there will be (should be) a 3" nosing or 5" landing tread that wraps around the open area and first step down. One never knows if that mitered nosing is square to any walls. My focus would be getting that exposed nosing area to fit up nice and tight.

Are you saying I should use the stair noising around the stair landing to find my 45?

IMO the stair nosing is not a good place to lay off of to get the 45 for all other areas. I have found most of the time a 3-4' stair is not square to other areas. And ofcoarse if it's off a hair, your off big time in the other areas. Also it's a short distance to figure layout from. When your running planks parallel to the rooms, it's another story. It's desirable to have a full plank at the nosing. If THIS was the case, it's simple to lay the first section across the Dining Area with a full plank at the nosing.
But considering a 45 and the layout of the areas, I would go with #2. When I get to the nosing I would square up the nosing by dry laying some 45 ends at the nosing, then securing it. When I start installing that section my starter boards are going to fit nice and tight against the nosing.
At the guard rail it's just a matter of adjusting the mitre saw angle for a tight fit.

If I might suggest that you set the line to run parallel to the wall or island that is in the centre of line 2. To me that will be the focal point of your layout and if you need to trim a board against it at an angle that may look strange. No one is going to notice if the floor is 45 degrees or 48 degrees but you will notice an angle cut at the wall/island.

Excellent point Keith, that would be an eye sore if the planks didnt run parallel to that wall.
Hopefully that wall is close to 45 degrees. If a little off, it would just be a matter of setting up a jig on the mitre saw for all the cuts, (if the angles sharper).