It should be noted that this is an in-game team, and most in game teams, (especially in the more recent games,) can and will work.
I'll take this one step at a time.
Incineroar or Primarina:
As with most starters, this is your choice. One way or another your starter is a powerhouse.
I can immediately say that Oricorio is pretty bad. It has 70's and 75's across the board, (BST) with slightly above average Sp.Atk and Speed. While 93 Sp.Atk is not bad at all for an in game team, the rest of it's stats, (specifically its bulk) is lackluster.
Between Raichu and Vikavolt, Vikavolt is probably a little bit better. Raichu is fast and powerful in Sp.Atk, but has a serious drawback in Defense. Any Earthquake will kill Raichu. While Vikavolt has a really poor Speed Stat it makes up for it in Sp.Atk with a whopping 145! After given a Quick Claw, Vikavolt can do really well in an in game playthrough, (except for Hapu.)
However Raichu is known to have a pretty terrible moveset. It doesn't learn a single move after Level 1. Unless you want to hold on to a Pikachu until Level 32, when it learns Discharge, you'll be stuck with Electro Ball. It does learn Psychic upon evolution, which is good. Vikavolt gets a great moveset from Charjabug, learning Crunch, X-Scissor, Spark. The TM for Thunderbolt can also be accessed by the end of the first island. Vikavolt is probably the better choice after given a Quick Claw.
Lycanroc is a strong hitter, and can definitely do some good, but Incineroar and Vikavolt cover all of it's STAB super effective hits.
As for Toxapex/Bruxish, you can use either one. Toxapex is definitely built to be bulky, with a Defense stat of 152, and a Sp.Def stat not car behind. It's made to be more of a wall than an attacker, so if that's not what you want, Bruxish is definitely your attacker. Even though it has slightly sub par stats, Bruxish has an incredible movepool and adds a Psychic type to your team. I would choose Bruxish for an in game team.
If there's any more questions please ask!