My house was built in 1920. To retain the original character of having been lived in for 90 years, we scra-pe away the loose paint and leave the imperfections as long as they don't stick out. We do fill screw holes. Since most of the trim was oil based, we prime with Zinnser oil based primer then top coat with latex. The walls can be treated the same way.

Its an old home. Embrace the history.

Behind the stove you can add stainless (somewhat hard to keep clean looking) or porcelain sheets pre-made to fit. Usually you can find such sheets in stove widths at appliance stores or in the range hood section at the big box stores. You can get one to color match the appliances.