I just finished the main storyline, and I'll share my lovely teammates here:
1. Popplio / Brionne / Primarina
I am always biased towards Water starters (with the exception of being Gen 5), and not surprisingly I decided to start out with Popplio. Once in its final stage, it becomes a monster - capable of learning many good moves such as Sparkling Aria, Moonblast, Ice Beam, Psychic, Hyper Voice and Energy Ball. Oh, and its unique Z-move, Oceanic Operetta, is really powerful too (not to mention, it has an awesome animation)
2. Alolan Grimer / Muk
Grimer evolves at Level 38, so its going to take a little bit of time for it to reach its full potential, but when it does - it tanks hits and strikes hard (although as a Grimer, it can still do some good work in the Grass Trial). Learns Gunk Shot fairly early - which is a plus, and it gets access to quite a bit of useful moves including Knock Off.
3. Bounsweet / Steenee / Tsareena
I'll admit. This thing didn't really impress me as a Steenee - and it was considered dead-weight on my team. But when it evolved into a Tsareena, it began to murder things left and right. It's got a base 120 Attack, which is nothing to be laughed at, and the Bounsweet you get from the trade will always be Adamant, so there will be additional power. Sadly, its got a pretty shallow movepool - with only Trop Kick, High Jump Kick and U-turn being decent.
4. Stufful / Bewear
OMG THIS IS SO CUTE. To be very honest, when I first saw Bewear, I thought it would be quite a mediocre Pokemon - but I was very, very wrong. It's got a really good ability in Fluffy - which halves the damage taken from contact moves, which means even super-effective contact moves will not do as much damage to Bewear. A solid 125 Attack with access to Hammer Arm, Superpower, Brutal Swing, Rock Slide and Swords Dance (which you can get the TM rather early) is also charming for this pink bear (and did I mention how adorable it looks as it pops up when you open Pokemon Refresh?)
5. Alolan Vulpix / Ninetales
As much as I hate to say this, Alolan Ninetales is probably the least useful member on my team. It's an extremely beautiful Pokemon, but unfortunately thats about it. 81 SpA is pretty mediocre, and while it has decent SpD, its HP could be better. On the plus side, it does get 'okay' moves such as STAB Dazzling Gleam, Ice Beam as well as Extrasensory and Hex. Breeding Nasty Plot seems like a must, since otherwise its not going to be hitting as hard as it needs to, even if the attack is super effective.
6. Mimikyu
Another mon which I thought would be quite 'bad' but it turned out to be quite useful! An extremely unique and helpful ability, while having access to many good moves such as STAB Play Rough, Shadow Claw, Shadow Sneak (priority), Leech Life and Swords Dance, makes it a really good teammate. The downside is that it took me FOREVER to find despite having a 10% encounter rate.