Run the long edge of the tiles down the long edge of the hall and into the bathroom.

I like a stacked pattern (is it called stacked when it's on the floor? In any case, the grout lines lined up with each other not offset). It is more modern and clean looking. With your size tile you have to stack it or do a 1/3 offset; the tile bows so offsetting by 1/3 allows the lowest and highest pints of each tile to be nearer each other, minimizing lippage.

It’s really about your preferences. In this case I would stagger the tiles - however the tiles should be with a straight edge.

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If you don’t finish getting that asbestos backed vinyl off the floor and properly prepare it, and use a tile leveling system, you are going to have major issues installing it any which way you try.

The TCNA recommends no more than s 1/3 offset for LFT, with full backbuttering using a medium bedding mortar. This isn’t for a first time tiler. If you don’t know what the TCNA is, hire a Pro who does. And be careful with that asbestos, using proper remediation techniques.

Most people would prefer to restore the original wood under that vinyl. Making that substrate ready for tile is going to mean removing it back to the subfloor and building back up correctly for tile.

I would hesitate to do large format tile in a house this age there will be movement in the floor and cracks in the tile in no time. Use a small hexagon tile in the bathroom and continue the wood in the hallway. Stop touching and scraping that asbestos floor and just put the wood right over the top of it.

I'm sorry but where do you all get that this vinyl is asbestos backed? Is it a vinyl you're familiar with? I've seen vinyl like this that was put down WELL after 1985, and didn't have any asbestos in it whatsoever. That said, it should be removed before tile goes down.

I’m older than dirt. I’ve seen that exact pattern and exact color in 1973 vinyl with asbestos backing. Of course, it should be tested. But removing it with abatement protocols won’t hurt anyone. Unless they don’t know what those are.

Is that original hardwood I see under the vinyl? If so I would forget about tiling the hallway all together. Restore that wood and then tile the bathroom! It will make the whole house feel larger!

When I suggested running it the long way I was considering the best look for the bathroom beyond too. I like a long edge to run into the room. It will make less cuts by the tub too so the edge is tidier.

I don't know how wide the hallway is but to me the layout looks very chopped up since there's only one full tile in each course. With the 1/3 offset that an amateur should probably use it will be even choppier. It will be one large format tile next to a sliver of the other. The pic Bill posted is beautiful, but it looks like the hall pattern follows the pattern that was chosen for a larger space.

That's why I like the stacked pattern here, running the length of the hall and then continuing into the bathroom.

PS my first choice would be restoring the wood if possible though :)