BM Palace White is a favorite of mine, using the color on walls in satin, trim in semi-gloss, and ceiling in matte. The different sheens make their own subtle contrast and leave your spaces with "the sky's the limit" choices on furniture, art and décor. Congrats on the beautiful new home!

damaged walls? maybe a more explicit explanation could help with the need for the undertaking. the home seems tasteful..rather neutral already. For me; I'd get my furnishings in....get area rugs in the strategic areas, [ ?replace the cocoa carpet in living room-is it worn?] , as I'm sure area rugs were not left and you need certain sizes for conversation/hallways/under table etc. That is quite a bit to do, it will help you with your palette, before you embark immediately on "facelift".

My current favorite wall colors are Behr Honey Infusion, Honied White and Yucca White.

I think a creamy white will be good. Get some large pieces of foam board and paint good size area using sample jars. Lowe's sells Sherwin Williams sample jars for a reasonable price ($3.50, I think). I have a cream with a touch of beige to set off the white trim and it works well with my warm wood cabinetry. Another color which works well with warm wood is sage. If you are partial to grays, consider a sage with a more gray undertone as cool grays do not work well with warm woods, but warm grays, which often read green can go very well.