One of the main reasons to get involved in the fleet battles is to eventually start collecting Zeta mats. Your first goal should be to get below rank 500 or 200 in fleet arena, this will greatly accelerate how fast you level up your ships. Next, develop a plan for how you are going to defat the highest level of the Ship Building Materials challenge and then the Ship Ability Materials challenge. One needs light side ships, while the other needs dark side ships.
When picking ships to unlock, make sure to consider the pilot. The pilot's power makes a huge, huge difference in the effectiveness of the ship.
By far, the best ships in the game are Bigg's and Vader's.