I have about 15000 for remodeling to do kitchen and other parts of home.

Knock down wall or just remove desk built ins? Paint cabs a gray. Get darker gray slate tile lay in a random pattern. Hardware should be brush nickel. Long 5" pulls. Lowes sells. Granite a light background with some gray. Keep all finishes same brush nickel.

Recess lighting is the way to go.

i see no reason to knock down that wall. its not going to gain you any work space. or cubboard space, I would remove the uppers over the island. take out the desk and put in a pantry there. Or actually move the fridge to that space, and extend the counter top over where the fridge is now. remove the table from the space, and put a larger over hang for an eat at island. if you had a larger budget, i would actually remove the island all together and expand the kitchen into the nook.

If the wall is load bearing, taking it out may not be an option. I would recommend taking out the desk part and putting in floor to ceiling cabinetry there instead and pull out the small, over the counter cupboards. That will really open up the space. You can either go for a darker stain or paint the cupboards and changing the drawer pulls will really update the cabinetry. Recessed lighting would be lovely, but if it's not in the budget you can find a more updated fixture. Make sure to update the floors along with the cabinets for a completed look. Good luck!