With Slayer, it's recommended to mainly melee your tasks, while you use a cannon, and burst on the burstable tasks.
Melee is the most popular main style, due to its low cost, although ranged is another fairly popular option.
Magic is not recommended as your main combat style, and it should only be used when bursting.
Now let's talk about melee combat.
The best in slot for melee is the Fang, which is only 30mil right now.
The Rapier, Inquisitor's Mace and Blade of Seldor are all second best in slot, and a cheaper option to use is a regular whip, which costs 1.7mil right now.
As with melee armour, it's important to have the Dragon Defender unlocked.
A Black Mask or a Slayer Helmet is also essential for Slayer training.
The best in slot melee gear is Torva, although you can get away with a Fighter Torso and Obsidian Plate Legs as a far cheaper option.
On some Slayer tasks, you'll want to wear magic defensive gear.
Masori is the best in slot, but Dragonhide does the trick.
Don't use Armadyl, because it gives a negative melee attack bonus.
When slaying, for a lot of tasks, you'll want to use Protection Prayers.
After the Slug Menace quest, you can use Proselyte, which gives the highest prayer bonus.
Monk Robes are second best, and they give the same bonus as Initiate and God Vestment Robes.
With ranged, if you cannon as many tasks as possible from level 1 to 99 Slayer, you'll get over 90 ranged.
This assumes you're using melee as your main combat style.
But if you do choose to use ranged as your main style, a Bofa, a Blowpipe or a Magic Shortbow are the best.
As with ranged armour, these are the best options to use.
Masori is best in slot, although Black Dehide is a cost-effective option.
You should always use an imbued Black Mask or an imbued Slayer Helmet if you're ranging.
The imbue gives damage and accuracy boosts to ranged, and it can be imbued at the Nightmare Zone, Soul Wars or the PvP Arena.
For magic, you'll need a set up for bursting.
For a weapon, you should bring at least an Ancient Staff to autocast Ancient Magics.
The Kodai Wand is the best in slot, currently costing 83 mil.
For mage armour, Ancestral is the best in slot, and God Vestment Robes are a good option because of their prayer bonus.
You should have an imbued Black Mask or imbued Slayer Helmet as well, plus always bring an Occult Necklace.