There have been many, many threads on equipment for Firestorm Citadel. Try searching Google for something like "spiral knights forum FSC loadout". The short version is:

You want normal, shadow, elemental, and fire armor. The specific choice depends on how laggy you are, what weapons you bring, whether you're solo or in a party, how experienced your party is, etc. Also, you can trade some protection for offensive bonuses, as Battlegrinder suggested. For trinkets, most players would go for offensive ones.

You want elemental weapons for most FSC monsters, but piercing weapons are better for trojans and Vanaduke's body. Your weapon for Vanaduke's body should be a gun, unless you're experienced. If your party is doing the Shivermist Buster tactic, then your weapon should have a big charge attack, because each time that you break the freeze should really count. Hence Blitz Needle is popular. Many parties skip Shivermist and just use lots of Blitzes. Solo players sometimes use mobile guns such as Polaris, Storm Driver, Argent Peacemaker, Valiance, etc. Weapons with big charge attacks are also nice for trojans and slag guards.

I would never wear Dread Skelly, but it's not bad, so go ahead. I would never wear heart trinkets, but health is helpful, so go ahead. BTB and Polaris are fine, unless your party is doing the Shivermist Buster tactic.