I think the conventional advice is to choose your cabinet color first, then paint the walls, but in this case I'd have to paint the walls first. You'll need to prime them regardless, so get them to a neutral white color and then decide. The red is so overwhelming it will make other choices impossible.

Leave the cabinets wood, and paint the walls. You may need two coats of primer over that red.

Definitely paint walls and I think if you added a backsplash, hardware and some nice lighting, your kitchen would be updated without all the trouble and cost of painting the cupboards.

I love the red, but I don't love it with the wood cabinets. If you can afford it, refinish the cabinets a darker color - walnut or dark cherry. Or better yet, get new doors. The sloped ceiling and red have a modern vibe that would go better with slab front cabinets and more contemporary hardware. As for backsplash, I love my back-painted glass. It's so easy to keep clean. If it is in the budget, I'd do a back painted back splash in the same red .