IMO first fix the lighting , as for the cabinets you paint them before choosing counters and back splash and paint color are the last items you choose.You need pot lights in the space I sure hope that door is being removed since it blcks the fridge the range is a very dangerous spot Maybe before spending the huge $$$$ on apinting the cabinets you think about a new layout for this space . I think a rework of the space would be ahuge improvenment and BTW acabinet refinisher is what you need not a regular house painter . You have really gone at this backwards so now stop and think before doing one more thing ,

As well as fixing the lighting, I would get a can of white or off white primer and cover those yellow walls before making other decisions. It is hard to make decisions with such a bold color in the space.

I think the order you have things is is correct, but your cabinets don't look that bad in the picture. I can see why you are refinishing the floors. Both previous posters have good points. I don't know why the frig is behind the door to the basement, and the yellow is very vibrant. How you proceed depends on how long you think you'll be in this house. Unless you're going to be there a while I wouldn't go through the trouble of painting the cabinets. When done correctly it is very time consuming, and expensive if you're paying someone to do it. If it isn't done right you will have something that isn't as nice as what you have now and the paint will start flaking off in a year or two.

If you replace the counters they will come with the sink if it is an undermount. You can supply the sink, but the fabricator will attach it.

After floors, if you are not changing the cabinet layout, I would have current backsplash demoed and pick out countertops. Especially if you want anything other than a solid color countertop. It is much easier to pick a paint color to coordinate with a countertop you love than to pick a countertop you love to coordinate with a very specific shade of cabinet. And it is very expensive to properly recoat cabinets so you don’t want a do-ever. Backsplash last. Wall paint very last

What I would do with money saved from not painting cabinets. I immediately thought of your kitchen when I saw this one--new countertops and backsplash, under cabinet lights, pot lights, pendants. Spend $$$ on stainless appliances. Get a tall counter depth fridge to line fridge up with pantry cabinets and remove cabinets above fridge. If you can spare the space by seriously downsizing, remove upper cabinet next to window and add open shelves to let light from window pour into the kitchen.

French Country Kitchen Cabinet Restoration · More Info

Install a barn door where your door opens in front of the fridge. Slide door to side of fridge.

Swap lower cabinet next to stove to the right of it or move it across the way to add more work space. (We need to see space next to kitchen. Please add another photo.) Then get a lower cabinet and put it to right of stove so stove is moved away from doorway. The utility lines are probably already there, so you probably won't need to run new gas/electric lines to stove.

Concentrate on having a light, bright modern dining area. Show us that space for suggestions for furnishings.

Sorry, I didn't answer your question at all, but I couldn't help seeing other ways to deal with the space.