I'm not sure that which end you start at really matters, so I would
probably start at the easy end as that's where you'll see more of the
floor and you want to get that right, rather than have it exaggerating
any discrepancies that start at the kitchen end. I'm sure you'll find
a way of attaching the bits that are partially under the units.
Undoubtedly there will be purists along who will tell you that the
boards should run lengthways, but that might be looking for trouble in
a space this size and shape.
Wherever you start, of course, you'll find that nothing is square but,
sometimes, making the floor square can show up the out-of-squareness
of the room even more.
Not sure what you mean about the cutting: I would definitely stagger
the joints, for integrity of the whole floor, but the only cuts you
need to make for this are at the ends of every other run and these
will be hidden under skirting or quadrant, so they don't have to be
I use a regular fine wood blade in the jigsaw (no doubt a laminate
blade would be better) and cut from the back so the saw pulls against
the decorative face. The only cuts that should show are those around
door frames though.
Good luck (!)