The Disgaea anime is absolute shit, and completely inaccurate.
NISA started with games, as far as I'm aware. NIS has it's own Universe where canon exists (think Marvel or DC, here).
The must plays are (Chronology):
La Pucelle Tactics
Disgaea: Hour of Darkness (Or, if you're a PSP or DS kind of person, Afternoon of Darkness)
Phantom Brave
Makai(/Phantom) Kingdom
Disgaea 2: Cursed Memories (If you're a PSP person, get Dark Hero Days, instead)
Soul Nomad: And the World Eaters
Disgaea 3: Absence of Justice (If you have the PSVita, get Absence of Detention)
Disgaea 4: A Promise Unforgotten

As well as a few more. Any game listen BEFORE Disgaea 2 will be rare, but worth it. NIS has been my favorite franchise since I was nearly eleven years old, and nobody has beaten them yet.