So many ways to approach this. Profit is when you can sell an item for more than your costs of production and marketing. Obvious but important. You need to sell the product. Typically that means reaching out to the market and convincing them to buy your product.
In our
permie context I suggest reading some of what Adam Klaus has to say on the subject. He makes some great arguments for persuading markets to pay a premium for premium products.
Again, simple and obvious, but for most of us really hard in practice.
You need to know both your market and your product.
Costs of production. The bigger the animal, the higher your production costs are likely to be. Not just feed or animal purchase price but infrastructure - fencing, shelter, processing.
Risk - bigger animals means fewer animals means loss of one is a bigger hit. Bigger animals are riskier for the farmer's health too. A cow can kill a person. A goose not so likely (but they may try!).
Learning curve on animal husbandry and associated costs. Easier and less expensive to work out the general principles with a few
rabbits than a few beeves.
Personally, the plan begins with small livestock that will not break the bank to house, feed, shelter, process and where I win any confrontation without a doubt.
Chickens, ducks, geese and rabbits. I can get multiple functions, provide most of their food, and get valuable experience in principles of animal husbandry.
Not likely to get rich off them, but will eat well with variety.
Down the road a little come sheep and goats for dairy, meat and fiber. Pigs fit in along the line as well, if only because bacon is awesome;)
I do not expect to try cows, I see them as not suiting my scale of operation.
Long winded point, one needs to know the business, whatever business, to make a profit. Learning the business can be expensive, especially if you go right to big ticket items for your learning phase.