Yes paint white and remove carpet. Paint is cheap as are professional painters. Painters charge what, say $60 per hour so just work out how long it would take you to do it and include setting up, cleaning before and after, any prep work, etc. Then multiply by 60. If existing floorboards under carpet then that would be terrific. Otherwise if no floorboards then it could not be so straightforward. Too difficult to estimate costs really as we don't know how large the spaces are.

Such a beautiful house, loving the high ceilings and all the timber. I also have a black kitchen and I think the black will beautiful with all the timber. I would go black but add a touch of timber as your accent colour. I have a black kitchen, white tops and timber insert shelves. Don’t fight it, embrace it. When its all done, you may just paint out the ceiling beams in white. Love your house, have fun.

the beams are the whole architectural focus in house of this style. I can understand people wanting to paint when the ceiling is low and flat as the dark timber can feel intrusive. once painted, the home's point of difference will be lost forever. maybe you should get a designer decorator out to your house, who has worked with style before - they will probably have some great suggestions for other ways to capture more light, through light furniture, reflective surfaces, window treatments, different lighting and mirrors. skylights do make a world of difference too🌞

If you’re tidy with your painting you won’t have to touch the beams to get the look in your inspiration pic. (Maybe a good dust). That way you can live with them for a while and change in the future if needed without any waste of effort. It’s a great looking house.