A Companion can only equip to a maximum of each of the following. In the case of magical items that require attunement, if you can get the creature to concentrate for an hour, they can attune to it during a short rest. If not, you'll need to find another way to "force" a creature to attune.
1 Barding (armor): Small/Medium is standard rate. Large creatures cost 4x the same cost as humanoids, Tiny creaturs 1/4 the cost.
1 Weapon: If the creature can be trained to use weapons. A wolf that is trained can use its mouth to hold a blade and use it at a disadvantage, A monkey can beat someone's ass with a club.
1 Cloak/Shoulders
1 Necklace
1 Headwear
1 Gloves/Bracers/Boots: 2 Legs/arms: Standard rate, otherwise mutliply the standard cost by how many pairs of legs. A Beast of Burden can't equip both bracers of defense and horseshoes of speed, you gotta choose one of them.
4 Rings: Also known as Bangles, cost 4x the price of a ring.
A Normal Quantity of Beast Organs.