In real life, I'd probably limit myself mostly to Normal-types to avoid hazardous situations (like house fires or getting electrocuted). Maybe Grass.
Furret and
Leafeon immediately come to mind. I can clearly imagine Leafeon basking in sunlight coming through the window.
I also enjoy bugs, but I don't imagine they'd like my living conditions too much (I spend a lot of time indoors). An adult antlion did sneak into my room before though, so maybe
Vibrava?
I once dreamed that I had
two Persian irl, one normal and the other Shiny. That was pretty cool. I'm used to the fickle nature of cats (I have a lot of cats), so I don't think I'd mind having a couple of these around (as long as they're the size seen in the anime and not the size of a lion).
Eevee would probably be my next pick, but one member of its family is probably enough due to its rarity. I could also see myself with a Porygon/Porygon2 since I spend a lot of time on my computer, but I get the feeling that those couldn't be found in the wild and would be VERY expensive. I'm a bit torn for my last one, but I've been wanting a pet skunk for a while because I think they're adorable, so I guess I'll go with
Stunky for my last choice. (I just hope it can control its stench and only use it in the direst of situations!)
However, in a world where any Pokémon could live peacefully with people and retain their cartoony features, things like burns and lightning strikes weren't very dangerous, and I did a lot of traveling (in other words, if I were a Trainer in the anime), my team would be a lot different. How many times has Ash taken a Thunderbolt or Flamethrower and fully recovers in like... 4 seconds?