It's tempting to paint so that you finish a section of the picture at a time, but that will necessitate a lot of brush washing and waste paint. Rather paint one color at a time, from the largest areas of this color to the smallest. Working from the top of the painting down helps prevent accidentally disturbing wet paint.
By starting with the larger ones you'll be more practiced using the brush and paint by the time you get to the smallest areas, which can be quite fiddly to paint. Painting by Numbers is an excellent exercise in brush control. You know exactly where the paint should go and so can focus entirely on getting it down there, and only there.
Having the brush control to paint accurately up to an edge or specific point is a crucial skill that every aspiring artist needs to develop. You'll use it, for example, when painting a background behind an object, adding color in an eye, or darkening a shadow of a vase, and wherever you want a hard edge on an object.