When to start gearing a new team?

I like to at least get a squad up to gear 11 before moving on, and take them to 12 if deserved. If you focus your Empire gearing to 11 and then start working on another that you're interested, you can always take Empire to 12 as needed, especially if they'll be your arena team for a while (a lot of them are pilots, so gear 12 is extra helpful). You should try to get R2 with your Empire team (Thrawn helps a lot with this).

Bounty Hunter's are useful in multiple modes, fun, and will unlock Chewie. Nightsisters are fun and useful, too. You'll want a Rebel team, so maybe think about farming Biggs/Wedge and Stormtrooper Han/Leia/Old Ben (these three, along with Farmboy Luke and R2, can get you Commander Luke Skywalker). You have a lot of options, but like others have said, do what's the most enjoyable for you. I like to play fun squads but there's some that just have a lot of utility and will open more doors for you.