Both can look great, it really depends on what look you are going for. Are you updating the entire room?

I'm all for white paint 100%. I like Simply White which is a fresh yet warm white. Benjamin Moore OC-117. Post afters if you go ahead!! Just leave those double doors to the dining room in wood. And consider painting the front door black.

I'm going to say don't paint the wood, but maybe paint the white-ish ceiling an ocher color like in the following photo and get some more colorful accents like throws, pillows, curtains and throw rugs. I think painting the wood white with your beige carpets would be too much beige and white (unless your paint them dark gray like Hannah) and no one would be able to remove paint from wood.

[https://www.houzz.com/photos/dining-lower-whitefish-lake-1-rustic-dining-room-minneapolis-phvw-vp~797572[(https://www.houzz.com/photos/dining-lower-whitefish-lake-1-rustic-dining-room-minneapolis-phvw-vp~797572)

I would paint the china hutch wall a dove white to start and see if that is enough. The sides and beams the wood may be just enough wood to keep some charm.

paint