Aside from the floor (which doesn't count because it's just a generic floor and will disappear if you put anything interesting anywhere else in the whole room lol), you've got 2 strong clear colors, black and white. I would not use a subtle, muted, or subdued color. I would use something powerful enough to hold its own with black and white, probably a warm color, a cool color would make the room a bit chilly. You might think about a clear yellow or green, maybe a pure red, or a lacquer red, or teal. Have fun!

Do not be embarrassed about your kitchen! You have chosen to stay home with the kids - more important than cabinets any day. Normally, I don't encourage cabinet painting, but your finish is worn and that is the time to consider it. I have white appliances and I love them - I will never do stainless. I have a friend with a newer white kitchen and she has white appliances. There is nothing wrong with white appliances. Turn off HGTV:) Just make sure if you go white, that it works with the appliances. One of the fun things about an older kitchen is you can get creative with it, especially if you are at all open to cottage style. You can have the center panel of one or more cabinets removed and replaced with glass or for a farmhouse touch, chicken wire with fabric shirred behind it. It is hard to make an older kitchen look modern, but if it is your style, it is easy to make it sweet and cozy. I would not do a countertop paint - they don't last and your present counter is fine - it is not bright orange or red so leave it alone:) I retrofitted a plate rail in one of my cabinets - if you want info just ask: from Pinterest If you have any sewing skills, you can make a faux roman shade for the window. I also have no problem with your signs on you soffit. I have plates on mine. Your kitchen should express your style and be unique to you: My faux roman shade, plates on my soffit and white appliances: https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~110720042 If you don't go with white, consider a soft green: Another thought since you have kids is white uppers and navy or royal blue or gray/blue lowers - might be easier to keep looking nice with kids. An inexpensive backsplash is the textured, paintable beadboard wallpaper. I don't generally like faux products, but this is good, inexpensive product ($20 Lowes), and very easy to do. Beadboard wallpaper backsplash: I used it in my basement kitchenette: https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~65270573

Looks like an open concept. Whatever you do in the kitchen will extend into the adjoining room. What color are the counters? They look green?

Our kitchen has oak cabinets and we cannot replace the cabinets now. I read that to “work with” them teal/green/blues generally work well and minimize the orange tones. I ended up using Benjamin Moore Green Wave in my kitchen (and Opal Essence in the adjoining dining room and living room that get a little less light but also has oak furniture). I have been very happy with both colors. Not sure if they might have too much green to go with your backsplash but might be worth looking at.