IMHO, the better direction for all the rooms except the center hall would be north/south(bottom to top). That center hall will look better with an east/west direction pattern. If the planks are tongue and groove on all four sides, the direction can be changed 90° simply by changing the direction. That allows for seamless(but visual) changes to be made in doorways. The change of direction for the entrance hall to the center left hall would be on a line parallel and even with the left entry wall straight across to the family room wall. Transitions in the rooms off the center hall would be made in the centers of the doorways.

Some might scoff at real stuff next to fake, but I have a few areas of real next to fake in my home which look fine (stucco next to hardie board, real marble next to fake ceramic marble tiles, and wood tile next to real wood to name a few). My wood next to wood tile is running the opposite way and I think it looks fine and was a good tradeoff considering the functional improvement tile provides in combined kitchen/mudroom area and the difficulty of matching 100 year old douglas fir, however 1) The opposite direction run makes sense for the orientation of my kitchen, that is the tile runs with the long dimension of the kitchen 2) Its at natural room transitions, not an abrupt change in an open room 3) The two woods are clearly different from one another so not trying to "match" per se and missing but they are in the same tone family, that is (to my eye at least) both are a neutral brown without any significant grey/red/etc. 4) I carefully picked a tile with some texture to look similar to the 100+ year old original floors. In your case, I'm not sure it works so well. Seems like you have grey "wood" joining with the actual reddish wood in what seems to be an open(ish) area. Also one is sort of a distressed rustic sort of look whereas the other is a shiny smooth (I assume prefinished) look. Seems like you already bought your tile, not sure if you have the opportunity to still change your mind. If you are 100% committed to the floor, I'd do them opposite directions.

Sorry but the LVP/LVT or even SPC/WPC product needs REALLY FLAT! Oh...no. The wobbly subfloor = DEATH to vinyl click ANYTHING. Why? Because the click edges are VERY THIN. Any bit of height variation will cause EXTREME stress on the click edges. Any stress on those thin, brittle, finicky, nasty edges and you LOSE the floor's integrity. And you lose warranty. And....and....and. I'm in Vancouver BC, so the extra $5K for subfloor work (by pulling the old floor, etc) doesn't even phase me. Cost of labour in Canada runs (roughly) $50/hour in the building industry. The sheet plywood is STAGGERING right now. Unless you purchase DIRECT from a mill (in small town Canada, that's ENTIRELY possible) you are looking at $3/sf for plywood alone. A tile install normally runs (all-in...tile+labour+materials) $18/sf and up...with prep being the extra (which is why he's saying DOUBLE the cost). Sorry but the 'lay it right over' the old wobbly floor is NOT correct. Everyone will tell you, "You can float it over anything," but they FAIL to mention the old floor MUST BE LEVELED and with a flatness rating that is ACCEPTABLE to the flooring manufacturer. I'd be happier with a STURDY laminate (except this is in a wet area) or an engineered hardwood (watch out for the clash) over vinyl being floated over wonky. Vinyl CANNOT HANDLE the floor height variances. The edges are too fragile, too brittle and too easily damaged just by standing on them over that wonkiness. Do the work. Pay the price and get the correct floor. If not, then just throw down any old 'King of Floors $0.99/sf vinyl' and be happy if you get 10 years out of it. You will replace it by then anyway, and you can pay for the subfloor work at that time...if you need to cap your costs today....but you WILL pay for it tomorrow. It's your call.

Are you planning on using the SAME vinyl in the living room? If you are, then I HIGHLY RECOMMEND you purchase ALL the vinyl at once. I know. That's a big chunk of change...but here's WHY: Man made products like vinyl (engineered hardwood, laminate, etc) have a 'shelf life' of 2 years (or so). That means it is produced, sold off and then NEVER TO BE SEEN AGAIN! Yikes! And NO ONE knows WHEN your chosen vinyl will END it's run. No one. Not the sellers. Not the distributers. Just the factory manager, and she isn't allowed to divulge that information. So...if you WANT the same vinyl in kitchen and living room, you are BEST OFF to purchase it all at the same time. As for transitioning, I'm assuming the laminate is floating. And I'm assuming the vinyl is floating. That means BOTH of the floors MUST be allowed to float. To do that, they must have a minimum of 1/4" - 1/2" of space between them were they meet. Must...Have...There is no way around it. None. Oh...wait there is. Glue down BOTH floors. And then you can do what you want. But that's a B!tch to remove at a later date. Remember: purchase it all RIGHT NOW if you plan the same floor throughout.