We have posted a very brief read list for jumping-point Jason Todd in the first post of this thread. If I recall correctly, it's Batman: Under the Hood plus the RHATO vol. 2 (Rebirth) up to now. For something more thorough, you can read RHATO vol. 1 (new 52), Red Hood / Arsenal (DCYu, if I'm not wrong. Poeple like it even less than his N52), Countdown to Final Crisis (people often hate that book, but his multiversal trip was actually fun) or his run as Robin pre and post crisis that we are reading currently in a thread, also linked in the first post of this thread. A Death in the Family is an important story for him, obviously, even if it's retold in other places and it hasn't aged well. Also, Batman: The Cult is a pretty cool old book that has Jason being very badass, and has some awesome art. There is more stuff (if I recall correctly, he shows up in Winick's Outsiders, and his Green Arrow. Also in Batman and Robin Eternal, etc.), books in which he appears for a brief role or he is supporting cast.
But Under the Hood + Rebirth is what I would go for a starting point too, honestly, even if it skips a lot.
And yeah, I'm totally skipping Jason under Morrison tenure over the batfam, because either he was barely him (many fans often joke about Redhead Jason being an imposter) or his role was really small.