A good horse or mule is great, but they just don't work for everyone. They take a lot of off-season care and money to start with. If you only want pack animals for hunting, they're an expensive way to go. If you ride year round, that's another story.
So, for occasional meat packing - you might be better off with goats or llamas. They won't carry the loads a horse will, of course, and you can't ride them, but they do have advantages. Most experienced pack goats are dairy breeds. That doesn't make them the best, just the cheapest. Male dairy goats are throw-a-way so they're recruited for packers. A meat breed wether, like a boer or Spanish will be bigger with heavier muscles and will carry more weight. They're hard to come by, though, because most of them are eaten before they grow up.
Llamas are very easy to care for and easy to train. Like goats, they can be hauled in the back of a pickup or even a van so a stock trailer isn't needed. Good used pack saddles are hard to come by so be prepared to spend a couple hundred each if you can't find used or make your own. Same for goat saddles.
Goats will be eaten by about anything with teeth. Llamas will run coyotes off and in a few cases, guard llamas have also run off bears (but don't count on it). They're no match for a cougar or wolf, though, but horses have also been on the menu for those critters.
A big meat breed goat will haul as much weight as a big llama, around 80-90 lb max for long trips. Both will go places that only a fool will take a horse. The problem is that you have to hike there yourself. If you don't want to lead a llama into a hell hole, don't shoot an elk in there.
The weak point on llamas is the legs. You have to learn what's good or not. Many have weak pasterns that will give them fits as they get older. Good legs will give you a packer that will last 10-15 years. A good back line and shoulders are also required for maximum loads.
Not too many years ago, a young llama would set you back a thousand or more. These days, you can get a male weanling for around $100. He needs to be 4 years old, though, before you can really load him up. That's no different than goats, horses, or mules, though.
Llamas are very easy to work with, but there are some rules. You won't need to be shown twice that when you work on one's feet, you snub up his lead so he can't turn his head toward you.
Also, when one is PO'd, they can make some of dangedest noises imaginable.
