I would suggest a cream or a beige color. It should keep some warmth in the room, unlike white which can be a little too bright in sunlight, and will make the room feel a lot bigger. A creamy color should also compliment your furniture well. If you were looking for a slightly brighter color you can always compromise! Cream walls with painted stencils in your desired color will brighten things up.

I would suggest a medium to light shade of brown. Browns go really well with lime green, plus the natural light will really bring out the warmness of the color. The only thing I would also suggest is to have some other accent color in the room. (lime green to match the hall is a good choice, or other fairly bright color) This accent could be in the from of perhaps a table cloth, wall hanging, pictures, candle sticks etc. This would not only make the accents pop and make the room eye catching but also prevent the room from looking too monotone with the brown wall and oak furniture. Happy painting.