Gary, what you've mentioned is exactly what got me hooked on the TWD game. Aside from the seemingly endless supply of ammo, the situations, decisions, and characters interaction is harrowing.
The game follows the story of Lee Everette, a convicted felon on his way to a Georgia prison when the cop car he's in crashes. After shooting the zombie cop that attacks him when he regains consciousness, he sets out into a nearby town, only to find it nearly deserted and full of zombies. When he finds a girl names Clementine whose parents were killed, he decides to protect her.
The goal of Season 1 of the game is to survive and protect Clementine until you reach Savanna, from where you'll take a boat up the coast to escape the apocalypse. Your heart gets broken again and again along the way, and it ends when,
I found it one of the best games I've ever played. It's a choice-and-consequence sort of a game, so there isn't a ton of action, but nonetheless, it's downright powerful.
I'll try to get into the show. I'm not sure when I'll be able to, though.