Which light armor for an animal companion provides the most protection for the least amount of ACP?
Barding provides the same protection as armor of the same type, so:
- Padded/Quilted Cloth 1AC+8 Max Dex/0ACP
- Leather/Rosewood 2AC+6 Max Dex/0ACP
- Hide 3AC+4 Max Dex/1ACP (3-7 AC/P)
- Studded Leather/Parade 3AC+5 Max Dex/1ACP (3-8 AC/P)
- Wooden 3AC+3 Max Dex/1ACP (3-6 AC/P)
- Chain Shirt 4AC+4 Max Dex/2ACP (2-4 AC/P)
If you really want to reduce the ACP, you can purchase/make Masterwork Barding for 150g; this will reduce the ACP to 0 for all but Chain Shirts. From this data:
Leather provides the most AC with no ACP (non-masterwork)
Studded Leather provides the best ratio of AC to ACP, (with the added bonus of the highest Max Dex available)
It wasn't necessarily part of your question, but it's good information that's related: for things you would typically supply barding to, you do not need Armor Proficiency if your ACP is 0. The only penalty for non-proficiency (above typical armor penalties) is that the ACP applies to attack checks. If your ACP is 0, there is no additional penalty.
Masterwork Armor increases the cost by 150g (ask your GM if this is increased by the unusual shape/size chart) and reduced the ACP of armor by 1. Any Light armor except Chain Shirt will have no ACP if it is Masterwork, making Studded Leather the definite best.
You can purchase a Mithral Chain Shirt for +1000g (again ask your GM if the cost is increased by the unusual shape/size chart) which will have 0 ACP, making it the best option.
One more option has come to my attention: Darkleaf Hide is Medium Armor with 0 ACP, 4 AC +6 Max Dex. So for an agile companion/mount, Darkleaf Hide is the greatest AC/ACP ratio assuming we can make ratios with a denominator of 0. It should cost about 1500g.