My best advice for Skeletron is to build the proper arena first. What I found worked best for me was starting with your standard highway. Fluff it up with, say, 2 layers of wooden platforms as high as you can reach for about 75-100 blocks. From there, build a small section of roof about as high as you can reach from whatever is going to be your top platform.
The only real important thing so far is that roof. That roof will be your life-line when he starts launching homing skulls. I would recommend building a staircase both directions at least as tall as the player right in the middle of the roof so when you run around the roof to avoid him, if he starts shooting again you won't take what'll be an easy shot for him.
With that, if you want to make things really easy, build a staircase of platforms on the side away from the dungeon entrance going up. Go up half a screen, build that platform out a small bit in case you need it, then continue the staircase up going back towards the dungeon. This is to help you make a big circle around Skeletron as he spins and rushes you, so you don't have to rely quite so much on proper timing of a second jump.
As for gear, the shield of cthulu has never failed me, barring that first boss fight ever with it equipped, heh. The main thing about Skeletron, though, is that the only real way to get away from him once he's on you is to move vertically; jump or fall. Don't ever try to dash and don't even bother running because you won't work up enough speed for it to matter before he kills you. Jump or fall. But with this simple arena, he should never even get the chance to hit you with his skull.
Definitely use the molten set for the armor. It's expert mode so armor is far more important.
You need boots and a double-jump item for obvious reasons. A grav potion can be good but watch the fall damage and don't get yourself trapped under the roof while trying to escape with it.
The shark tooth necklace is only good if you use really fast-firing weapons. The best thing to do is get the bee's knees from queen bee and pair it with the hive pack, also from her. This weapon finishes expert pre-hardmode and lasts a little way into expert hardmode.
Of course in expert mode always make use of buff potions. Ironskin, regen,
endurance, wrath/other (depending on what you got), archery for the bee's knees, and of course swiftness isn't a bad way to go as well and of course eat some food because it's expert mode (pumpkin farms are really easy, quick, and cheap to make too, but bass are more than plentiful). Stock up on honeyfin as well!
The last accessory is up to you, if you have the worm scarf use it, though the goal here is to not get hit
My advice for fighting any boss for the first time is to first learn to survive, then learn to damage while surviving.
