Strictly speaking, the most efficient way to go initially is to farm 5 dark side ships (to get Executrix to 5* for the highest tier fleet ability challenge) and 5 Rebel ships (to get Home One to 5* and unlock Chimera). However, you will probably find you need more than these ships or need their pilots leveled and geared very well in order to do everything you want with the minimum. Home One upgrade challenges are particularly difficult.
I can say getting 3 stars on the highest tier fleet ability challenge (requires Executrix and 8 other ships at 5*) as soon as possible will be very helpful if you want to be competitive in arena, since that will get you zeta materials. As one of the last players in my arena shard’s top 50 who still doesn’t have any zetas, I can tell you the right zeta can change a battle.
