You have a wonderful lot of storage. I also don't find your cabinets objectionable. I think the builder grade oak cabinets are the ones that have given oak such a bad name. There are some very nice, different style oak cabinets like yours that are quite lovely. I agree with the lighting. I would say holes in the drywall would be better than such a terribly dated, dirty looking (nothing personal, I think all those of that style look dirty) box light. It just cannot be your style! I have a hard time speaking to color online, given different monitor resolutions. Green to gray would probably be lovely with your countertop, but gray to me wouldn't compliment what I'm seeing color-wise of your cabs. Green? As long as it didn't have a yellow base. You've got lots of potential there! :)

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.

Consider a warm white paint, that is on trend, and would lower the contrast between the oak and the walls........possibly a blend of the lightest color in your sofa? find a rug that is done in a tweed effect; cost effective and lots of choices that will work with the warm oak trim. Also you have a lot of room on either side of the fireplace; consider putting the TV on either side down low over a console? Or if you are considering new furniture place the TV on another entirely and see about doing a sectional that embraces the new TV location and the fireplace. win win. Some examples of TV to side of fireplace in rooms with multiple windows and some nice furniture arrangements. Go big or go home!

Here's a timeless Houzz article about wall colors that go with wood trim. Your trim looks great, and you'll be saving yourself a lot of time and hassle by painting the walls instead. https://www.houzz.com/magazine/11-terrific-paint-color-matches-for-wood-details-stsetivw-vs~9025200 How about a new larger painting in this palette for over the fireplace when you're done? Here's SW Greek Villa in a room with golden oak features: Another way to pick your paint is to match the lightest color from your stone then go way, way lighter. Just make sure it harmonizes with the trim. Avoid a stark white and go for something warmer.