Don't race to build new buildings. They are a REAL headache because they're far apart - so the more you have, the more scattered your "guests" are. You have to run from building to building to feed them all. This is especially true for the cats, dogs and horses, because none of these animals keep their food IN the building! You have to trudge back and forth to the main building to restock your food supply for one particular animal type.

A "step" of a house just makes it larger, so step 1 of the small animal house only holds a few of each, while step 2 is a larger version that holds more animals.

Small Animal House
This holds your rabbits, guinea pigs and budgies. Step 2 makes the budgies in a separate cage, which is a pain because now you have to go in and out two separate doors to take care of this group of pets :)
Step 1 - 550
Step 2 - 300

Practice
This is your home. Really this is just about ego - it doesn't help anything at all :) When you upgrade, the rooms just get larger. Which, really, means it takes longer to walk around.
Step 1 - 1000

Cathouse
The place that cats hang out. I won't comment on the name, other than to say Nintendo should have used an English speaker to name this building. Why did they put it by the parakeet cage??
Step 1 - 600
Step 2 - 300

Kennels
Where the dogs hang out. You can only walk one dog at once! Why can't you walk multiple dogs - or let them out into a run? Start your dog walk at 19:59 - it lets you finish the walk, so this lets you "stay up later".
Step 1 - 700
Step 2 - 300

Stable
Where the horses hang out.

Therapy Center
By the order of these and of the training sessions, you might think this was about the massage only. But really, until you build a therapy center, you can't start looking at horses. This is where you examine the horse.
Step 1 - 800
Step 2 - 1500
Step 3 - 2100

Pet Vet Walkthrough

Paws and Claws - Pet Vet Review