Following are rules related to PCs and animal companions. These rules are outside any magic or class abilities.
Animal companions must be acquired by purchase, breeding, trapping or similar technique. Without special ability or skill, a PC may only manage a domesticated animal bred for companionship. That is, dogs and cats, not snakes or fish. Typical companions behave according to their nature and may obey simple commands within the limits of their limited intelligence and their relationship with their owner.
Animal companions do not have levels or gain XP. They can be taught new tricks. Owners must spend a month with a new companion after which the animal will obey simple commands to sit, stay, come, heel and leave it. Obedience also depends on context and owner charisma. A month of training may add another trick.
Animal companions require food and care. The amount of food depends on the size of the animal. Care and attention varies by animal as well, but any neglected animal will eventually lose the bond with its owner.
Ordinary animal companions are dogs and horses. Although rare, cats and rats can be kept as pets. Many other domesticated animals, such as pigs, are impractical as pets. Some exotic animals may be acquired in certain locations. Those would include monkeys and parrots.