The Death Guard were once the XIV Legion of the Space Marines, and fell to Chaos during the Horus Heresy.
Led by their Primarch, Mortarion, these bloated, disease carrying warriors worship the Chaos god of decay and filth, Nurgle.
Whilst technically Chaos Space Marines, and thus able to ally with them on the battlefield of Warhammer 40k, the legion has access to many units unique to them thanks to the gifts bestowed upon them by their benevolent god.
The mainstay unit of the army is the hardy Plague Marine, able to shrug off even more damage than a regular Chaos Marine. Deathshroud Bodyguards and Blightlord Terminators exemplify this trait and push it even further, being some of the toughest infantry in the game.
Even the vehicles of the Death Guard aren't free from the taint of disease, with Plagueburst Crawlers firing payloads of daemonic spores into the enemy, and Foetid Bloat-Drones floating around the battlefield spitting toxic slime like a horribly mutated plague fly.
For a painter, this army offers a lot of opportunity to really get stuck in with things like weathering techniques like chipping and rust, as well as coating models in slime or gore. There's really no 'wrong' way to paint the Death Guard, as a messy and sloppy paint job actually does them a lot of good!