The hardwoods are extremely valuable. I would work in a medium brown that eliminates all yellow/orange/red. To do that, the stain will have to have a green undertone. That means a specialized mix for your situation. A HIGH END hardwood flooring professional can do this for you. It will take a couple of weeks to find the right colour/mix. The professional will come in and strip a section of flooring (like 20ft x 20ft). S/he will then apply different stain mixes to this area for you to view. You will then choose the colour that is the best fit for your situation. At a mutually agreeable time, the professional will come in and refinish the entire house - including the stairs (quite expensive but well worth it). The banister can then be stained/painted to match the hardwoods. The only time I would look at moving away from hardwood is in the DEEP south or in very hot climates. And it would be VERY helpful if the entire house was built on concrete and not wood joists. Tile is very heavy. It often requires wooden subfloors to be beefed up (decrease the deflection rating = no movement that would damage the tile). The wood is worth saving - unless you absolutely hate it (disregard the colour). If you love tile and wish to have it everywhere, then go for it. But realize that hot climates are some of the few places where this is considered normal. Everywhere else (any place with "winter") would find this a nuisance should you wish to sell the home. Besides, you mentioned budget. Ripping out the hardwood and replacing with tile would be double the cost of refinishing the hardwoods.

Now that you have lived in the house for two years, you will have figured out if the kitchen foot print is usable. As soon as you start renovating this kitchen, you will be tempted to change things. Little things. Things that have bothered you for 2 years but could do nothing about. Once you do that, you have a new foot print. And then saving the boxes will be irrelevant or impossible (depending on how much of a change you make). Because change is inevitable, you will want to plan this out CAREFULLY. You will need to figure out your floor plan FIRST. Then you can look into whether or not it makes sense to keep old boxes vs. starting new for a full upgrade. If a bigger change is going to happen, you should get a certified Kitchen Designer on board. S/he will save you plenty of money with her/his designs and abilities. The KD will put together a package for you, including colour palette, flooring and counter top materials. Which you will direct the KD to order for you OR you can source yourself and then have installed. At which point, the flooring is decided WELL before the kitchen is touched. As you can see, you have a few more steps to go before you worry about flooring colour. To decide now, before you have a full idea of colour/materials would be putting the cart before the horse. Floors go in last (and can be chosen last). It is an important thing to work with. As tempted as you are to get rid of the red vinyl, you will be very upset to pay for a floor TWICE (which is often the case if flooring is changed before the kitchen is renovated). Because you have vinyl that is EVEN with the hardwood (same floor height) I would look at very thin product. It will prevent a large 'lip' from occurring through the doorways. But that's a decision that can come LATER. Right now you want to figure out the kitchen's footprint.

We have hardwood throughout our main no tile at all. Is that an option ?

Seeing the furniture, I going to say no to white. A natural oak would look nice. If you did upholstered, I would stick to gray, and matching the grays could be tricky. I've seen YouTube instructions for a DIY tufted headboard that didn't seem too beyond my modestly handy skills, which would give you more flexibility in choosing fabric colors. If you want to buy, I'd be very cautious about mail order (online photos are very unreliable; maybe you could find a supplier who would send you swatches on Etsy or somewhere). If you shop locally I would find a paint swatch to match the furniture to carry around with you when you shop. https://www.amazon.com/Jezebel-Headboard-Christopher-Knight-Home/dp/B06XB6MH4X https://www.article.com/product/16708/lenia-white-oak-queen-bed https://vermontwoodsstudios.com/products/copeland-linn-oak-platform-bed This is from a UK site, but Vermont Wood Studios has a similar bed (found it after I did the mock-up) https://theoakbedstore.co.uk/products/boston-solid-natural-oak-bed-frame-4ft6-double