I tend to prefer my zombie stories without the twist. George Romero got the formula right in my opinion.
Having said that, one
very popular zombie book is Brian Keene's
The Rising. I abandoned it, but I appear to be in the minority.
A father is hunkered down, trying to survive the zombie apocalypse, as you do. His wife and son are out and he's given them up for dead until he receives a phone call that sends him on the road to find his son.
Another one that is different is David Wellington's
Monster Island. It's basically Escape From New York if the prisoners were zombies.
If you don't mind reading comics, you might like
iZombie. The series deals with Gwen Dylan, a zombie gravedigger in Eugene, Oregon and her friends Ellie, a 1960s ghost, and Scott, a were-terrier.
Gwen can pass for a regular girl, but she needs to eat a brain once a month to keep from losing her memories and intelligence. When she consumes their brains she "inherits" part of the deceased's thoughts.
iZombie was turned into a TV series, but I never watched it.