Nute Team

Long term, your Nute team will include Nute, Dooku, Wat, Asajj or Jango, and a tank (side note, I love ST Han for this role especially with Wat). In the meantime, the answer is essentially just any Separatist.

Your staples of the team will be Nute and Dooku going forward. You want Nute there putting out extortion and doing what he does, and you want Dooku to help keep the heat off everyone but the tank with his stealth as well as stuns. Grievous will do fine here, but he doesn't hit his stride until at least you put down the three left side pieces at G12, and by the time you get there you're probably already well on your way to a droids team, so that essentially eliminates all of them from this team. But until then, he'll do fine.

I keep Jango with the BH, because he's just a much better lead than Bossk IMO. If you are going to run him with Nute, then consider Embo and Zam for the BH team. Zam fits better under a Bossk lead, but you can't ignore Embo's damage and dispel on basic.

And you said it yourself you've seen the team with Nest and that's because she just works really well with them. Dooku can stealth everyone so opponent's have to hit her, if you're running a fast nest slowing down the enemy team with extortion makes her better, and all the other good things that come with Nest.

It's a great team, and one that still gets taken too lightly

I enjoy this team on occasion. I need to get the left two to G12 at least and B1 into relic land for better damage, but it's fun and I'm sensing some opponents don't know how to approach it.

I'm thinking of including Wat Tambor in mine. Currently still starring him up though.

Nest is better for offense in lower divisions as she can solo entire teams. In higher divisions this isn't so common anymore as there are way harder teams. In this case she fits perfectly into a Nute team that's full of seperatists so a fast Dooku will take all allies except for Nest into stealth and your opponent might have to stick attacking to Nest if he doesn't have a mass dispell at hand.