Overall: Farm your empire of empire is what you love! But try to toss your spare energy at Old Republic characters when you can. They’re key to branching out
Characters: Don’t bother upgrading units that aren’t immediately useful. Resources are precious, as are credits. It’s better to focus on one group that’s strong than a ton of characters that are weak.
That aside there’s 2 empire teams available.
Imperial troopers: which includes Veers, Starck, Snowtrooper, Range Trooper, and a free slot (most use death trooper but it’s very out of reach for a while so magma/stormtrooper works)
Palpatine Empire: Palpatine, Vader, Tarkin, Thrawn, and Imperial Tie Pilot. This one is the one I think you should go for. Aside from being much easier to farm, you’re well on your way to getting Thrawn and Palpatine. You’ll be given lots of shards as you level up for Vader, while Tie Pilot is a cheap farm and comes up in the ship store and Tarkin is in the arena store. Aside from packing more of a punch than troopers (for now) it doesn’t take much to get them going.
Ships: farming Tarkin is a good idea for his ship. But generally tie pilots ( empire and first order ) work well for assists. And you’ll get plenty of Vader’s ship shards but it doesn’t hurt to buy some if they show up in the ship store