This looks like a nice little project. I like the step thru frame, kind of important as a person gets a little older, I think. Inexpensive v-brakes wouldn't be too bad. If I remember correctly, your spindle should be marked and if not then measure it. The size should be in millimeters. You should be able to replace with a sealed cartridge unit. I always take apart, clean then reassemble as well. I use a slightly dampened rag using mineral spirits. Rubs off grease and old unwanted paint from leaning up against fences, posts or other bikes. Won't help the paint chips. A similar color of fingernail polish can help. Once I'm done cleaning the frame I use cheap Pledge knock off furniture polish to polish the frame and fork. 3 times usually gets it looking oh so shiny. There are plenty of inexpensive Shimano parts available on line if you choose to replace components. Look for a smooth treaded tire for comfy cruising. If you go for the silver parts, good luck due to almost every component being black now. Best of luck. I think your mom will have a nice little cruiser/grocery getter when you are finished.