The new lighting could effect the wall color and the color of the wood - so definitely do that first. Do some research into the lasting effects of gel stain - I've heard both good things and bad things. Here are just some unasked for thoughts- if I was working with this kitchen on a budget, I would possibly remove the upper trim piece and the small wood piece over the windows. I might remove the entire cabinet to the left of the farthest left window and replace with some shelves. I would remove the over the range microwave, which being short I could not even use, and replace with a stand alone vent. You could do a stainless vent for a more modern look. It is more expensive, but you could stain an unfinished wood hood with insert for a more farmhouse look. You have so much lower storage I actually would be tempted to remove all of the upper cabinetry - especially if there is a pantry cabinet - I was wondering where the fridge is - is there a pantry cabinet next to it? As far a curtains - I do like the softness and color window treatments add, though tis is a person style choice. This vent is a little larger than you would want: Less uppers - pretty window treatment: Rustic shelves: If you like a bit of country / farmhouse, beadboard makes an inexpensive backsplash and works well with shelves - rather than tiling, which might possibly need to be redone if you got new counters down the road. This is my basement kitchenette - done very economically with some of my original cabinets (refinished), shelving and beadboard - though in this case I used the beadboard wallpaper to save money - might replace with the real thing in time: https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~65270573 My main kitchen is also oak and in my "my pics" idea book - if you want some possible ideas for counters/ backsplash / farm sink - but it is done in a vintage style.

I'm biased because I just finished painting my kitchen and hall this color but ... Eider white? It is a little warmer but also so pale you almost think it's white until you see it against white trim and ceiling. It does not read as beige or yellow at all to me. As to the cabinet color ... it all depends on your budget and if you like any of the woods that are available. I chose a stained wood because I like wood grain and wanted something super durable against dings and dents. Maybe see if they have any wood cabinets that are not overly red or warm, it looks like you really like gray so I'm guessing you like cool colors?

Bittersweet stem looks like a strong option. I was also looking at SW Ivoire. I tried a Malibu Beige on a patch of the wall today and it was horrible. Looked like gray putty. Again, no direct light past 10 am.

It's not just that the color is different with Red Oak, but the grain is busier too. With such a narrow plank, the effect with a very light Red Oak floor might appear choppy. I think the sample to the left of the island column is very even and complements the island finish well. Don't get hung up on trying to create a White Oak look from Red Oak. Look at what works best with the rest of your finishes, even if it is not what you had envisioned from the start. The two samples on the right look very pink and lavender to me. The one on the left looks busy.