God, my third one was already randomized and I got Jambette... please invite three villagers over to your island before you finish the houses.
I invited Nan. (She is not my favorite Normal. I did out of kindness.)
I invited Erik. (My favorite Lazy is Stitches.) But I do it because Erik is one of my favorite Lazy villagers—and I did not want to lose the opportunity.
I did not invited any Peppy villagers. I visited Nook Islands, rather loosely (and not on the hunt for specific villagers), and enountered separately Truffles and Anabelle. I did not invite either of them.
That was Day #02.
On Day #03 (for me, Saturday), I was informed by Tom Nook about three incoming villagers. I followed through with locations and building furniture (exterior and interior), and found out—for fact—the incoming villagers are: Nan, Erik, and Bonbon.
You are correct—if you don’t invite a villager of any categories of Normal, Lazy, and Peppy, the game will randomly assign applicable category/categories on Day #03 so you have to get established with that total of five. (This is before dealing with the remaining three categories: Cranky; Smug; and Snooty.)
- - - Post Merge - - -
Bangle, Rhonda, and Papi. I'm not terribly excited about Bangle, but I can always make him move later on, I'm sure. -shrug-
Bangle is a female.
This is a brown-furred, Peppy tiger. (Pretty good villager.)
After the starters are a Jock and an Uchi, the next group are a Normal, a Lazy, and a Peppy. (So, from the first five, you get three females to two males.)
Here is a link about Bangle:
https://animalcrossing.fandom.com/wiki/Bangle