Chickens and/or cow/horses.
Cows have milk which you can use straight away or it can be converted into stuff that can be stored for years(cheese - good stuff good stuff), and there are numerous ways to preserve meat without freezers. Smaller and more wilder versions like goats is also a legit and sometimes more convenient option
Horses pretty much the same - meat, blood, skin, etc - everything is useful.
Both are used for transportation as well, which survival-wise is helpful.
The best thing about them, they eat grass, and the grass grows pretty much on its own, at all places. (Winter however is a problem, as one needs to store that grass)
So yeah there are reasons why those animals were popular among nomads, in cold places where bananas do not grow, etc. In places where it is possible to have them, it is quite convenient to have them.
Chickens are another good stuff. They can't sustain themselves on the grass alone, but they bring eggs which shelf life is half a month easily, and those eggs can be a replacement for meat. And here is the good part - they can eat bugs and all sorts of insects and worms. They eat meat, including those you do not want to eat - spoiled a little bit. They eat plant food as well grass, seeds.
They are like pigs, you can feed them what you do not want to eat.
And here is a good part, one of the things you do not want to eat - insect larvae, fly of all kinds - there are many. Flies(and some other insects as well) are famous for eating things which, hm, how to word it, hm, basically only them eat that stuff.
You can convert trash, grass, plants, meat spoiled not spoiled - whatever you have - into worms. You can make worms out of all kinds of trash you can find around and have them being feed to chickens with grass as well. (Sure there are ways to do it good and right, and not so well. But there is youtube and there are videos on that topic. A keyword is probably - composting, chickens, soldier fly, red worms.)
Animals are in some aspects more robust in terms of environmental conditions, they have better immune systems, they heal. They are more forgiving of some mistakes. They can defend themselves or escape, at least the number of creatures wanting to eat them are lesser in numbers.
For a variety of reasons, including - one chicken(for lack of words and simplicity) can get you 50-150 new chickens a year - chickens are better than garlic.
Animals, in general, are the way to convert inedible vegetables to edible stuff, and they are ready to do so from the get-go.
Things are not that simple, but nomadic tribes which did and do have animals are proof of viability. Animals allow people to survive and do pretty well in places like extreme north where most of the year no plants are growing at all, not even winter garlic of yours.
Next best option is hunting-gathering - really nothing new, good old still the same.
- okay, seems there is a need for some
There are around 250 recognized breeds of cows, for all sorts of purposes and with all sorts of properties, they even have a mini jersey cow, the size of a dog(a very big one), lol, how much better it can be.
But here American Milking Devon this is the gold, this is a cow for those who wish to survive, like OP, this is the cow of settlers since the 17th century. Its purpose and goal and properties is to survive and let people survive with it as well. It is a multipurpose cow. It not best at milking, meat quantity, but it good at eating whatever is available grass, saplings, or whatever it finds to chew on.
It is a healthy, well-established breed, probably a bit in decline those days but. So if you decide to take a cow for you to survive - you take this one.
difficulties raising animals
It is a truth that a novice has 50/50 chances to kill an animal this or another way by his care, especially ones which are not suited for free-range, or in circumstances when such option is not available, or productive breeds.
I assume wilderness is freely available there, no charges, no money, and only one's efforts, self-reliance, as survival in stone jungles is a whole bunch of a different story.
There are easier breeds, there are more demanding ones. There are different goals for them. Never you take for survival productive breeds, especially modern ones - be it for milk, be it for meat whatever they made for it implies good care, and for good ones it implied you will do extremely good care and assumed you do know exactly what you do and have access to all sorts of modern stuff. They require special care to achieve the performance(and some just to stay alive or not become crippled), and not necessarily do good without it, they not necessarily healthy ones, they won't survive in wild - humanity goes puff so will they as well. But there are robust ones, and those are the valid option.
There are animals and breeds of those which are easier to take care of. 10000 years of selection weren't for nothing.
are plants better?
No, it is categorical no, period.
Why? The main problem isn't as it is the same situation for novice farmers to kill plants, or that if you noticed something wrong it is too late, and not that plants can't moo to you hinting some problems.
No, the problem is that even if you experienced farmer, decades of experience, the whole life you live from land - the result isn't guaranteed. Even today, even on farms which plant stuff day in and day out for since the inception of the farm hundred few hundred years ago. The result isn't guaranteed.
There are few reasons for that. One of which - plants can't move. Not by themselves, not by your efforts.
You can think - it isn't a big deal, right? Well, it also means you can't cover shelter them in bad weather - hail, strong wind, strong rain, too much sun - those are dangers for plants which by nature have to be under the sky. And if it happens, and it does, then even today there is nothing of help.
Planting, as a process may be easier with today's technologies, but without it - if there are no animals to aid you in the process, planting enough will be pain in the rear. Not impossible. Harvesting is also a problem, and it does not come without work in between.
Plants are sensitive to the structure of soil (is it lose, is it clay-ish, is it...), to acidity, to other stuff. Sensitive to climate, how good was the weather for them, etc. Crop rotation, fertilizing, etc.
It can't run from insects, it can't outrun even a snail, which creeps on it.
If someone thinks it such a carefree thing, oh boy ...
There sure are good things about plants as well. So as for animals. And there are bad things about both of them as well.
But converting non-edible plant matter into edible stuff - there really something futuristic there in that.
If one can, take animals and plants.
If you managed both - animals your food from get-go. Do plant tpse plants as well and do pray they grow as you plan them to be.
Cows it for serious colonization, settlement, they not the best animals to get initially, but they can be a great help in planting and harvesting. The main reason for why not, because they multiply in numbers too slow.
Rabbits, chickens, pigs - those are fast guys. Out of those only rabbits can live entirely on grazing. Chickens are suitable for the free-range approach, but they need supplementary meaty stuff if they do not have enough of it on free-range. Worms can be one of the ways to close the loop on grass, and there are such examples. Pigs are the worst, works if you have enough food for yourself plus extra.
And only chicken(or any other egg-laying bird of that kind laying eggs once in a few days, which is not typical for any random bird) do provide food from day zero, and one can sustain on it fully and there is no plant alternative for such performance.