Don Y wrote:
We're laying tile throughout most of the living areas
(not bedrooms, carpet is warmer on bare feet!). I
think the tiles are 14 or 16" square (not keen on
unwrapping a pallet to measure).

I'll be laying them "diagonally" so the grout lines
are at 45 degree angles to the walls (regardless of
*which* wall!).

As the house will effectively be one continuous stretch
of tile, where you *start* plays a key role in what the
final result is like!

We have a bedroom hallway down the center of the house that
is a couple/three feet wide. I suspect having the tiles
*centered* in that hallway will be the most visually
appealing -- it would be too noticeable if they were offset
in any way (small space means small discrepancies are
very noticeable).

we have two other major "sight lines" perpendicular to
this hallway. One is a "virtual hallway" (a view
through several doorways/walkspaces -- even though there
is a wall on only one side of this virtual space) of
similar dimension. The other is a larger, "open"
hallway (again, with only one wall but much wider space).

My thinking is to create a centerline down the bedroom
hallway and another centerline for this "virtual hallway".
Where they intersect, lay the "key" tile. So, eventually,
a "row of diamonds" travels directly down the center of
each of these "narrow" hallways/sightlines.

Everything else will just end up whereever the tiles end up
laying (can't interrupt the pattern).

This makes the wide hallway a little less than ideal (the
"diamonds" wouldn't be exactly centered owing to the dimensions
of walls/rooms). But, it's a much wider space so hopefully
not as noticeable "off center" as it would be in the narrower
hallways.

It also makes the front entrance a bit wonky; the tiles again
not lining up nicely in that space, centered on the doors, etc.

I've been playing with alternatives using a CAD model of the
house floorplan (so, I can move the "grid" of tiles around
and see what they will look like relative to the walls and
openings) which is how I've discovered these compromises.

Is there some rule of thumb that governs how folks pick the
point for the "first" tile (even if it is not laid first)?

Yes and lay it first. One tries to make the edge (cut) tiles as large as
possible. One first lays out horizontal and vertical centerlines (or, in
your case, 90 degree diagonals), then dry lays to determine the starting
point (which should be center out) for both directions. The possibilities
for both directions are tile center on line or tile edge on line; it is
entirely possible that tiles along the horizontal line will be one choice
and the vertical the other.

That means that one treats each area as a separate entity which is not what
you want to do and which is IME and IMO a HUGE mistake. It is virtually
assured that you will wind up with untenable, unworkable situations. Much
better to treat each area as separate and lay the tiles to conform to that
area, using some sort of transition between areas.

In my case, the whole house is 12x12 Saltillo. I used two types of
transitions...one was square layed against diagonal but most were small
pieces (2" x 6") at the opening of one room to another, regardless of
whether there was a door at that opening or not..