I think it's a nice idea. I've always had houseplants.
Just go pick something you like, and look at the little directions that come with it.
I wouldn't take it personally if you kill a few at first, though. My advice that you didn't ask for: water them only when bone dry then let them dry out again (most houseplants, but not all.) I've lost many a houseplant by over-watering it.
It's not as easy as you might think! I actually think my cat has more predictable needs and she definitely is much more reciprocal in her affections.