eggshell and semi gloss are finishes, not colors. It sounds as if you are saying, eggshell is a warm color. There are soooo many whites. Just plain white on white is very sterile and IMO cold. If its a busy room or stair wall, I would do a slight "warm white" with an eggshell finish on the walls and a flat white on the ceilings. (flat is best for covering up imperfections on the wall, buts not washable in any way. If the room is not a busy room with kids and pets etc, you can get away with flat paint which is most hiding of imperfections but not washable at all.

oops, I just saw this & was going to suggest you add a little Grey Owl to white so that the ceiling wouldn't make the trim disappear. It sounds luscious!

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?