Just got Melia and I am trying her out as my main. Up until now I've been using Shulk, Reyn, and Sharla exclusively and now I switched to using Melia, Sharla, and Shulk. I just finished reading the guide for Melia, so hopefully I can do well with her.
Melia can do a
ton of damage, and is great against certain bosses/enemies who are resistant to physical attacks.
My Melia Setup
Weapon Gems: Electric Plus and Blaze Plus are the two most important gems for her, IMO. Back Attack Plus is
great, but you probably won't get this gem until a bit later. If you don't have a Back Attack gem, Poison Plus or Arts Stealth gems (if you find yourself drawing aggro often) are also excellent choices.
Armor Gems: Ether Up gems are most important, because they increase her damage. Other than that, Melia is squishy so give her some defensive gems. Early in the game your best defensive options will likely be HP Up, Muscle Up, and/or Ether Def Up gems. Later on you will gain access to the amazing Debuff Resist and Unbeatable gems.
Battle: Melia can have 3 "summons" (little floating balls) active at a time. Each has an aura that buffs her and her party members in some way. Summon Bolt, for examble, gives you an Ether Up buff, which increases Melia's damage output since she is an ether spellcaster. At the start of battle, I use Summon Bolt and Summon Copy to have 2 bolt summons floating around her, for a double Ether Up buff (they stack). Now I'm ready to attack.
*I use Summon Earth and cast it (using her Talent Art button) to inflict a long-lasting poison DoT on the enemy.
* Then I use Summon Flare and cast it to inflict excellent damage and a fire DoT. Then I use Summon Bolt and cast it to inflict a big electric nuke on the enemy. The rest of the battle I'll just switch off casting Flare and Bolt, and throwing in other arts when necessary (Speak Break/Reflection if I'm getting attacked, Burst End/Mind Blast during her Element Burst state) until the enemy dies. It's really quite simple!
*Edit: I should mention that using Summon Earth is not always necessary. Like I said, it inflicts a long-lasting DoT. This is great for long battles (bosses or unique enemies) but can be overkill for regular mobs that die rather quickly. So against regular mobs, just skip Summon Earth and go straight to using Summon Flare for its superior upfront damage AoE and DoT.
Armor: Armor with good physical defense is your best bet, IMO. Melia is a ranged attacker so she's usually outside of the range of enemys' AoE ether attacks. Weight doesn't really matter, since she is one of the least agility-dependent characters in the game — she doesn't rely on auto-attacks (agility affects your auto-attack accuracy) because she should be kept at a distance from her enemies. I put the Rafaga set on her because it's one of the best looking armor sets in the game, IMO.