Started with Rowlet, obviously. I named him Boko and he is simply phenomenal. Not only is Rowlet the cutest Pokemon ever designed, but it's pretty darn powerful too, and Boko's only grown stronger since evolving into a Dartrix. He was all I used for a while so he's a few levels ahead of the others. I'm trying to give him a bit of a rest, but I may need to rely on him in the next Trial too.
I was sure to catch a Mudbray as soon as I could. Luckily, the Pokemon I have named Onepu came with the new Stamina ability, which increases his Defense every time he is hit, which is pretty great. He came knowing Bulldoze, and it didn't take long to learn Highhorse Power (95 power, 95 accuracy); I didn't think he'd become a powerhouse until evolving, and now I'm almost afraid to see how powerful that'll make him!
I also spent some time getting a Cubone, Wargoyle. She's been pretty solid from the get-go too, though her typing is redundant with Onepu's for the time being. I need to be careful about evolving her--apparently Cubone from Alola only evolve at night, at level 28 and up, and since Moon inverts the time of day...I want to get this right so that she can evolve ASAP, and maybe take on the next (Grass-themed) Trial.
And just before logging on I caught a Wimpod, Podzilla. It was...simultaneously difficult and easy. See, to catch Wimpod you have to actually catch it. It appears on the overworld and runs into a hole in the ground as soon as it sees you, so I didn't intercept it the first time. But once I did, one Quick Ball was all it took, thank God, and though her moves aren't great I'm confident in saying she'll fare better than a Magikarp would, and I know she'll have comparable payoff.
I really, really want an Alolan Sandshrew, but those are on island 3 apparently, and then the last slot is reserved for Lunala. It'll be a Ghost-heavy team, but I'll cope.
One thing that bugs me though: when encountering wild Pokemon, they can now call for help from other wild Pokemon. This is involved in chaining for shinies and high IVs, which is all well and good, but when two Pokemon are out you can't throw Poke Balls. And once you knock out one, the other one can call out another Pokemon right away. And then do that again. And again. And. Again. It's really rather frustrating in practice, I've found. But the only other Pokemon I want to be absolutely sure to catch before beating the game is Alolan Sandshrew. Once I beat the game and start hunting to fill the Dex, maybe I'll have more capacity to be patient with this mechanic...and more powerful Pokemon who can wipe out reinforcements in one fell swoop.
So yeah, Moon is fun thus far! I'll make another post if I come across anything else I feel like saying.