I'm like you, in real life I LOVE pets. But, pets on the sims can be annoying. The only trick I've leaned is that it's easier if you have two of the same animal because they can socialize with each other. You really can't get away with more than one pet per sim, so if you only have one sim, two pets will be hard.
Another thing I like is when the pet has the lazy trait. They just lay around all day and they are okay with it. Holy alto adopted a Scottish terrier who was lazy and I never had a problem with that pet or had to get it another to keep its social up. It just chilled. And, I don't know this for a fact but I think maybe the loyal trait, make the pet get a higher reaction from social interaction with its owner, so I like that trait too.
Lastly, I've really come to love birds in the sims 3. My grandmother had birds and my fiancé will not allow me to have them ever so playing with them on the sims is a second best. The birds don't need as much but it's sad when they die, and they don't live that long.
JodySuzanne