Which ships to farm right at the start?

Unfortunately, you're going to have to farm more ships than you need for just your Arena team. A priority will be getting your Dark Side ships, so you can get Executrix and beat the Ship Ability Materials challenge, so you can speed up your Zeta Materials farming. If you want the Chimaera capital ship, you'll have to focus on your Rebels. You can put this off for a bit, though, as this capital ship isn't necessarily as vital now as it was back in Ships 1.0.

So, early on, you're going to want to probably focus on the easier farm Dark Ships, and build them to a certain level. Then, you'll probably end up "abandoning" some of them, while continuing to focus on others, and then you'll incorporate new ships. It's somewhat inefficient, but eventually you'll have enough to field at least two full fleets, which will be helpful in your Territory Wars, anyway.