I've always liked playing Animal Crossing sort of natural-ish with villagers. Gamecube, Wild World, and City Folk I straight up didn't care who was coming in or out haha. No standards. On New Leaf, I'd let villagers move in and out and would reset/trade for good ones but not really care if I forgot to fill a spot. It got annoying trying to plan where the houses fell, so I stopped even resetting for that.
New Horizons gives a lot more flexibility, but I still let all but a couple of my villagers move out when they ping me (unless they like JUST got here, then I wait for the next time) and try not to dedicate too much time to island hopping. I don't really set out with an idea of who I'm looking for. I just grab the first villager whose appearance I like. I've always been way more into the decorating/design part of Animal Crossing, though, so I'm not really the type of person to be like, "Oh I HAVE to have this villager." It's more like there's villagers I'd love to have come around, hope they do, and if they do and leave or just never do show up at all, that's fine, too. It keeps things interesting for me. That and randomly swapping villager house locations. Enjoy your new front yard, buddy. :d