The best animal is really no contest. Dogs.
A male cat is a fair idea if you want to keep down vermin. I normally don't bother.
As for other animals, the thing is, the food situation in dwarf fortress is just not hard enough to justify animals for food. Between slaughtering the pack animals, immigrant's animals, slaughtering wildlife (with hunters or even better military) and caravans (which always bring A LOT of food if you are low) you need never want for meat. That's not even accounting for farming, which especially with processing (quarry bush, sweetpod, booze cooking) and seed cooking can easily provide all the food the fortress needs.
If you bring animals it's for flavour and fps reduction so you may as well embark with whatever you like - the difference in value for points is not that great for most animals.
But dogs are good from a pure strategy perspective, I normally embark with 10 of them (5 boys, 5 girls), for a strict breeding program you only need one male, but I bring dogs more for running into battle and dying especially in the early game, and I don't want to max out my dog cap in one breeding season (not that there's anything wrong with that). If I hit a food crunch early on, and it happens, because I'm often lazy with food (relying on immigrant's animals and caravans) then I just slaughter a skinny, weak male dog to improve the genetics.
Dogs are great at generally making life difficult for thieves and snatchers, they can also distract ambushes and sieges. I basically make a lot of trainers (especially my important dwarves), and just let the dogs chase their trainer around. There are more organized ways you can use them but essentially I just use them for randomly getting in the way of attackers.
They are also great for savage embarks since a pack of dogs are a very good distraction for nasty megafauna beasts which can easily rip limbs off. Dogs have low lethality, so you really want a dwarf with a weapon for execution, but it's much better that the giant badger be wailing on your dogs, than your barely-armoured military dwarf. Avoid dogs and all other animals on zombification embarks.
On embarks with really rude wildlife (or undeadlife) the pack animals can also be used for defence, pasture or restrain them in the entrance and they might give an invader a lucky kick to the head. Horses and such are very powerful (I learned this when I stationed 5 dwarves with training weapons in a room with a wild horse), but they're cowards and run away unless cornered, so I couldn't recommend embarking with them for defence, but the freebie pack animals can be used that way.