I would recommend to tile a section of the entry ( unless you enter straight into the living room, then no) and then wood floors for the rest of the space. You can Also have tile in the kitchen area. It depends on the actual space, and somewhat where you live. Florida residents often have tiles in their homes, while people who live in cold climates generally don't.

You have: WARM travertine tile on the first floor. You have DARK warm wood cabinets. You have WARM countertops. The LAST thing you want sitting next to that BEAUTIFUL WARM coloured stone is gray. No gray. Nothing in your home says "I need gray to make it perfect". Nothing. Your furniture will change. Your area rugs will change. Your wall colours will change. They will all change inside of 15 years. But your PERMANENT stone or tile floors will STAY. If you must use a tile next to stone, I suggest working in the same tones. You can go darker or you can go lighter but stay inside the SAME TONES as the travertine. If you REALLY MUST HAVE GRAY - then rip out the travertine and start again. Gray and peach stone/tile do not like to play nicely together. It screams out, "I didn't want to pay to do it properly." I would recommend finding MORE travertine in a different sized tile and add it in at an angle (diagonal install). You can find a stone that is either a little darker or a little lighter. You can then add a decorative boarder to the rooms where you are installing it so that it looks like you did it on purpose. This is a great way to add more of the high-end stone to a space that already has high-end stone. But please do not add gray in with peach. They just don't like each other. Flooring snobs, like myself can see it right away. We KNOW when something has been done piece meal. We also know when someone did the piece meal NICELY vs. someone who did it without a thought to the overall look of the floor. Compliment the stone you are keeping. Let your area rugs turn the space gray. That trend is quickly dying. It makes sense to throw out a rug in 3 years. It doesn't make sense to rip out a tile floor in 3 years.

Are you also changing your counters? In the lighting in the photo the counters go even less with the cabinets then the floors do and you may get more mileage out of changing them. In fact I'm gonna say something a little controversial. From what little bit I can see of the floors, which I'm guessing are just linoleum, they look kind of funky and retro against those cherry cabs.

Have you spoken with your realtor about this? Honestly, giving cash back at closing for a floor allowance is appealing to a lot of buyers. Especially if you plan to live there while this work is done this may also be appealing to you - because, solid hardwood everywhere (except the bathroom with a tub or shower) is the most desirable for a buyer. I wouldn’t even consider a whole home in LVP as a buyer. Studying comps with your realtor and weighing that with your floor estimates should be considered. Feathering in new solid hardwood and sanding and staining may be the most cost effective if you have a decent amount of existing hardwood. If you are set on doing it I’d price three scenarios: feather in new hardwood and sand everywhere and stain, new engineered wood floor everywhere and new LVP everywhere (all in a very light medium brown). With the LVP you will have to put down new plywood everywhere which really brings the cost of that up so you may be shocked with the pricing studies.