King Slime is a very simple and easy boss, with loot that is mostly useless, so unless you want the Slimy Saddle or the Royal Gel I won't recommend wasting your time on him. But if you do, here's the gear you should use:
Silver or Tungsten Armour
At minimum. If you find enough Gold or Platinum to make their respective sets, go ahead and use that. But if you can't, try to get enough for these sets, don't use Iron or Lead Armour, because the extra defense will help in case you get hit.
Gem Robes
If you're playing mage, you should get one of these and use pieces of ore armour to fill the other slots, or put a Wizard Hat or Magic Hat in the head slot if you get lucky enough to get one. The extra mage stat boosts are worth it.
Flinx Fur Coat
If you're a summoner, you should replace the chest piece of an ore armour set with this, because the extra minion slot and summon damage is worth the bit of defense lost.
Fossil Armour
As a ranger, Fossil Armour can be a useful alternative to a set of ore armour, if you can survive long enough in the Underground Desert to gather enough Desert Fossil. However, its ranged-specific stats are rather low, so it doesn't make too much of difference.
Projectile Sword
Using a regular broadsword is a horrible idea. You'll take lots of damage from King Slime himself, and his minions will quickly overwhelm you. A sword that fires or summons a projectile, such as the Enchanted Sword or Starfury, is much better option. You could use the Terragrim, because of its high DPS, but you'd have to get Gold or Platinum Armour and be careful to not get overwhelmed by King Slime's minions.
Flaming Mace or Ball o' Hurt
If you can't get a projectile sword, a flail is probably your best option. While flails have low range, they have more range than swords and have decent DPS. They can also pierce indefinitely, which can be useful for dealing with the minions. On a Crimson world, the Flaming Mace is the best option. On Corruption worlds, you could get a Ball o' Hurt instead, which is better, but is harder to get.
Gold or Platinum Bow
As a ranger, one of your best weapon options is a bow. Craft a Gold or Platinum one, because it doesn't take too much of their respective bar and if you do enough spelunking you should find plenty of the ore. Frostburn Arrows are the best arrows for the boss itself, but Jester's Arrows are great for dealing with the minions.
Grenades
Grenades can be useful for dealing good AoE damage, however they are inaccurate and can deal significant damage to you if you're not careful. They also be purchased in large quantities.
Gem Staff
At mimimum, get a Sapphire or Emerald Staff, because the Amethyst and Topaz Staves are too weak in my opinion. If your world has Silver, you should try to get Tungsten from Crates, because the Emerald Staff has pierce, which can be useful for killing the minions, while the Sapphire Staff doesn't.
Vilethorn
If your world has Corruption, you may want to get a Vilethorn, because of its infinite piercing. However, it does have short range, which might make a Gem Staff preferable.
Flinx Staff
The Flinx Staff is probably the best summon staff for this fight, because it doesn't require much grinding and has very good DPS when combined with a Leather Whip or Snapthorn and a Flinx Fur Coat.
Vampire Frog Staff
This staff is better than the Flinx Staff, but it is significantly harder to obtain, because it requires a natural Blood Moon to occur at least once, and it is dropped by very strong and agile enemies at a low chance. I wouldn't recommend going for this staff at this stage of the game, especially since the Flinx Staff can handle this boss pretty well.
Leather Whip or Snapthorn
Your minions will greatly benefit from a whip, and you'll also be able to deal damage without relying entirely on your minions. The Snapthorn is the better option, since it deals more damage and gives the "Jungle's Fury" buff, but if you're having trouble getting the materials from the Underground Jungle you can go with the Leather Whip, assuming you have enough money.
If your world is flat enough, you don't need to build an arena, since the best way to beat King Slime is running away from him. However if your world isn't flat, a single long platform over any obstacles should do the trick. It can also be used to help get over the boss and his minions when trying to turn around.
