Sigh...sounds like you have someone who isn't willing to jack out 1200sf of tile (back breaking but do able) and then grind down the thinset and then fill the low areas (aka 'subfloor prep). Of course the COST is something most homeowners don't like to see on a 'job cost' proposal. Many a contractor has lost a job because s/he quoted the cost of the BEST PRACTICES option. So the installers have gotten smart and started quoting 'low ball' work. This is just to get them the job (so they can feed their families). But what that means is they are forced into the 'not great' practices. I always recommend the homeowners get a full quote for the job. That includes flooring REMOVAL and SUBFLOOR PREP (two different costs) and then the installation costs (a third cost). If they are purchasing the materials then material costs are another cost to be added. To jack out tile = $2-$3/sf. The subfloor prep can be another $2-3/sf (these quotes will always be a 'range' of cost because the installer won't know the amount of TIME it takes to do the work...some tile is SUPER STUBBORN and other tile pops off like Pezz candies. With a situation like yours, that would have added as much as $5/sf = $6,000 MORE than what you have already been quoted (I'm assuming some things here). My question to you is: would you have hired the person if they had quoted you $6K more than what you were offered? Now onto what is usually the best option: Remove the tile and prepare the subfloor for the new porcelain tile. Please ask your installer to draw up a NEW quote for those two jobs to be ADDED to your job and ask for a new time line estimate (could be 2 days or it could be 5 days...we don't know). And ask him/her if s/he has the ability (in their schedule) to revamp your job to suit the new requirements = remove tile, prep subfloor, install new porcelain tile. In other words ask for a new quote using 'Best practices' which include removing old tile and subfloor prep. You will want to see their reaction to this. They will either jump at the chance to earn another $5-$6K or they will scowl at all the 'work' ahead of them.

It sounds like you have a busy house but not a 'destructive' house (ie. 4 toddlers and multiple pets). I believe your house/family can 'handle' hardwood. You've lived with laminate before, so LVP isn't much different. It looks very good (as good as a good laminate). LVP rarely is allowed 'underpad' so the NOISE aspect is going to increase. Here is where LVP and laminate differ. A laminate can have a great underpad to help reduce noise transfer. LVP CANNOT! Oooops. There goes the bedroom concept. Hardwood (I prefer solid with site finishing) can have underpad like 6mm cork to reduce noise transfer. That means hardwood and laminate have MORE in common than laminate does with LVP. Even though laminate and LVP have the same GRAPHICS they are two VERY DIFFERENT products. If I had to keep budget in mind, I would purchase HIGH END laminate (like Patricia has = out of Germany) and use a HIGH END underpad. I would then use the laminate upstairs and down...and leave a carpet (or a runner) on the stairs. Remember: resurfacing the stairs to bring them to code will be the SINGLE MOST EXPENSIVE part of your renovation. The stairs can eat $10K all by themselves! Nope. I am NOT kidding. And remember: a narrow strip hardwood (2.75" - 3.5" wide) in red oak in character grade can be as little as $5/sf. Installation + finishing will add another $5/sf. The EXPENSIVE part of solid hardwood is when you try to get 'trendy' with them. Wide planks = very expensive. Special stains = super expensive. Etc. You can have a solid hardwood floor for roughly $10/sf. The stairs would be extra.

If you start laying the boards north to south, do that throughout the house; if you start laying the boards east west, do that throughout the house. As you decide how you want the boards, think about how you would want them in your living room -- or great room -- and why and then talk with your pro installing the boards and ask if that is the most practical way to lay the boards and, if not, why not. Go from there.

To the design question, of course you can have two different floors on two different levels. So long as the wood stairs match the 'main level' where the public would be most likely to be, then the private areas (such as upstairs bedrooms etc) can be whatever floats your boat. Lots of people have tile and wood on the main floor and then carpet on the upper levels. Totally acceptable. Now for the technical stuff. Vinyl has a chemical reaction to wood FINISHES. Yes. The colour you don't like is part of the wood finish. That colour has a tough finish over it (polyurethane). That polyurethane is most likely a petroleum product. The vinyl is 100% petroleum product. The two petro based products are going to have a chemical reaction. The wood floors will STAIN the vinyl sitting on top of them AND the vinyl is going to STAIN the wood sitting below it. Now for the MOISTURE issues. Vinyl acts like a water proof sheet. The vapour escaping from the wood below is going to hit the bottom of the vinyl. The moisture will be trapped. It will drip down onto the wood causing it to rot. Yah. Rot. So you not only have stained vinyl (ruined) you also have squishy, moldy, sticky hardwoods sitting below it (ruined). Now you have to replace both products. The advice = sand/refinish the hardwood on the main floor to a colour that works with the stairs. Average cost of a sand/refinish = $5/sf. It is one of the cheapest flooring 'purchases' you can make. Can you load a photo of the bad hardwood?