Dick Grayson became Nightwing during his membership in the Teen Titans (and the batman books around that time). So just a little bit before Crisis on Infinite Earths.

If you check the Robin (Dick Grayson) reading order, you'll notice that Nightwing: Year One bumps up against The New Teen Titans: The Judas Contract. If you want the bronze age take on it, I'd reccomend getting your hands on any New Teen Titans books you can, as they chronicle the history of the character coming into his own before and after he becomes Nightwing.

The Nightwing: Year One book is also enjoyable and a lot more modern in writing style. As a bonus, it's got a cameo from one of my favorite underused characters.

The Dick Grayson list isn't completely tagged yet, but eventually it will have all appearances of the character as Robin, Nightwing, and Batman (and anything else!)

Barbara is featured in Showcase Presents: Batgirl, Batgirl: Year One (goes along with Robin: Year One and Nightwing: Year One), the Batgirl OGN released in the 90s, and a few other random appearances. She's got her own Greatest Stories Ever Told coming out soon!

On the Batgirl Reading Order, all the appearances up to Zero Hour are Babs as batgirl.

Hope that helps!