Fixing damaged veneer

I recently bought a dresser and vanity from the 1940s at a thrift shop. I am wanting to sand and repaint it but it has some spots of missing veneer on it. How do i fix those and repaint it so that it looks good? The hardware on it and the over all condition is very good other than some minor scratches and a large dent in the top edge. I want to paint it a solid brown because of some of the deep scratches in the veneer.

If anyone has any suggestions on how to fix the missing pieces of veneer and the whole strips of veneer along the edge of some of the drawers, please let me know!