We don't eat meat, so no help there.
In the kitchen, we use a paper bag that we get from the grocery store to line the trash can. But, between eating leftovers, the dog, the chickens, and a full bucket a day of compost (no liner there), and recycling (paper, plastic, glass, aluminum) we only fill up about grocery paper bag of trash a week (for a family of 3 plus a teen on weekends).
My best advice is instead of worrying about the type of liner, worry about trying to cut back on trash through eating leftovers, eating more whole plants, composting, and recycling as much as possible.