I mainly use Executrix. Which capital ship to go next? Ignore Chimaera?

Since you are already building BH ships (all 4 of them, I assume) you may as well start building Home One and rebel ships as well to prepare for when you unlock Han's Falcon. The rebel fleet will be your next step to stay in the top ranks in fleet arena. You will pick up Chimaera at some point along the way even if you're not building towards it. It unlocks by using rebel ships.

I assume, you already gained access to the zeta ability materials challenge, since you have a 6* Executrix and at least 3 LS ships at 6* or more.