You need to do a little more archeological digging still. You need to know the whole construction of the floor before you can decide how best to install something new. I'd take up that plywood piece in the kitchen and see what's under it. It's higher than the surrounding floor, so needs to go. You should also be able to see from there what subfloor is under the original kitchen hardwood. It's too bad the space under your entryway is finished, but I'd still do some exploring from below to see what's under there, and to figure out the fix to stop it from squeaking. Is it drywall below or a drop ceiling? I know it probably seems like a pain to tear out drywall, but if you cut out a clean patch, like 2' x the width of the joists, it'll be relatively simple to repair. Just make sure to cut it down the center of the joists so that there's room to screw the patch piece to it later. Cut the hole under the area that squeaks the most, if you can. Have someone walk on and watch the floor from below to see what's moving. It might be as simple as pounding in a couple shims from below, or face-nailing a loose board from above. You want to find out what's underneath the hardwood. It might be laid directly on the floor joists, or there might be 10" wide boards that the hardwood is nailed to. Another thought is to take out a board in the hallway, since that's not original and you want to replace it. See what the subfloor is there. I am a bit puzzled at why, when you've stripped the kitchen down to the original hardwood, it's still higher than the hallway floor. Is your current surface perhaps not the original kitchen hardwood? Peeling back the plywood area will help determine that. BTW, I haven't heard of that stop squeaking product you linked to, so can't offer any personal opinion. And don't pour self-leveling compound over top of hardwood. It needs to go over plywood.

When it comes to hardwood, trends are something to ignore! Why? Because hardwood is pretty much a lifetime purchase, and unless yours is damaged in some way, you're probably not going to replace it. So, light wood vs. dark wood, wide planks vs. narrow planks -- that stuff's all going to come and go. With that in mind -- as well as the very real concerns about cleaning dark wood -- I'll vote for a nice, neutral midtone every time. Not too much contrast, not too red, and (unless it's a beach house) not too pale. I think this is the wood that's most likely to give you good service and stand the test of time.

Yes, it is being installed perpendicular. I know it's not the ideal... but in the interest of time and budget, it's what we've landed on. We are likely going to do an engineered floor on top, to eliminate a little bit of the extra height. I would (just for my own knowledge on what to expect) love to hear the cons of this method, even if we're likely to do it anyway :) And it is a wood subfloor - so just add plywood ontop of that until it becomes flush is what I'm hearing. Thank you!

Laying the new floor in the same direction as the old floor is not the normal way to go about this. In the building industry, it is more common to see layers that are staggered or "bricked". In other words if layer #1 is laid in a North-South direction, then layer #2 (the top layer) is laid perpendicular to it in an East-West presentation. If you want to run the new flooring in the same direction as the old, you will want to use some underlayment (plywood) over top of the old floor so that you can maintain the "staggered" or "bricked" layering system. That is one way to maintain the North-South presentation. Please work with hardwood flooring professionals who have some experience renovating these old gems. They will have seen what worked....and what didn't. Their experience will be invaluable on a project like yours.