Tutorial For The Twins
What I did to kill this boss is made 2 of each potion I needed-those were Gravitation Potion's, Ironskin, Shine, Night Owl(not necessary), and Hunter.
In this fight, armor doesn't affect you very much as long as you can dodge most of their hits, which is easy. I used Adamantite, but I suggest Cobalt or Mythril since this fight is easy. Weapon's affect you by a lot-you'll need a Megashark or a Crystal Storm to kill The Twins. Use the Melee Helmet, it gives the most defense.
Now, who to kill first? It doesn't really matter-I killed Spazmatism first since he's harder to kill. Leaving the easier boss for last is fun for me. But you can kill whichever one you want.
If you want to kill The Twins multiple times to get all of the items craftable with the souls, I suggest making the Fairly Bell first. It will help you get to start the fight faster since you won't need to make illumination based potions. Fairy Bell is much better than Orb of Light.
Hope This Helps :D!