Addressing the Underside Visual Advice

Went down to the shop today to clean up a bit and sat down to ponder addressing the underside of my 71 Demon (currently stripped down and on the rotisserie with the underside facing me). The car was originally a red and has been repainted at some time in it's life. She is going back yellow as my original one was. No real rust to speak of , just surface in places and old paint with dirty black undercoating in the fender wells and frame, very little on the underside pans and sheet metal. I can't remember what mine looked like back in '74 so I need your help and your advice on what you have done or would do. Removing all the undercoating seems to be a dauting task. I'm just having a hard time picturing what I should do and what it should look like when it is done. Please let the ideas and advice begin.