The first tab of the arena store is labeled, appropriately, "Arena". This is where you get essentials for the Arena.
Sands of War
The first, and probably most essential, item you can purchase is Sands of War. Again available in a regular or mega pack, there is no discount for buying the larger pack - it's just there for convenience. These use ironite as their currency for purchase.
These are cheap enough, but XP shards, or even XP, can be farmed easily enough. We don't really recommend spending coins on this one.
Similar to the Trooper store, you can buy rare, legendary, specific class and more. While it helps build your roster, weigh your need of these against what relics you need.
Just like in the Trooper store, Skill shards are a necessary evil throughout your playing of this game. If you have the coins and want it, we would never look down on someone for buying a Skill Shard. However, we'll again caution you to weigh the options with relics.