I like this question. It’s something I’ve wondered about myself!
I was heartened to see Michelle Arnold answer in Ask An Apologist, that works of mercy towards animals is a stewardly thing to do.
What further relieved me was the fact that our own Pope Benedict XVI has a couple of cats–at least in Germany he has one named Chico and another cat comes around to play with Chico who might as well also be his cat. I was at the Vatican this month and a tour guide did confirm that he’s got 3 or 4 cats and that they are building a new place for them. (This contradicting an older story I saw featuring an interview with Ingrid Stampa–but maybe it’s just a matter of the story being older than the newer news). Where we stayed on Borgo Pio, which is where the then Cdl. Ratzinger used to live, he was also known for feeding stray cats daily.
I wouldn’t try to be more Catholic about this than the pope is. Many priests have pets. Cardinal Mahony has two cats and another cardinal has a dog. And that’s just what we know about.
The catechism tells us not to accord the same kind of dignity we afford humans, to animals (something like that). I’m not going to pick this apart like an apologist because I feel assured that I don’t have to, seeing as even our highest clergy have pets. So I interpret this to mean, if you are in a situation where you have to choose between your kid and your pet, for example, you choose the kid. Like if you only have $3000 and both need surgery and you have to choose. The kinds of potential dillemmas you could come across ought to pretty much be no-brainers. I wouldn’t worry about them.
To what extent do you have to worry about spending too much time and money on pets? Ehh, I think you just have to feel it out. If a pet isn’t going to appreciate something like a diamond collar, it doesn’t seem like the way to spend your money. Just keep your pet reasonably comfortable according to its needs, and healthy, to the extent that the needs of others in your family don’t have to suffer. You can’t really say you’re morally culpable for “wasting money” on a pet when there are starving people in this world. If that were so, then why aren’t we selling off everything we own to the poor? While that’s a very saintly thing to do, we are not obligated to it to quite that extent. Pets enrich our lives in ways that really aren’t frivolous at all. Own them to the glory of God, to marvel in His goodness.