Disclaimer: This may not be the most efficient, best or fastest way to get to 99 Slayer but it is my experience I got from going to 99 Slayer. Feel free to comment below to improve this Guide.
While you can start Slayer at any point, I recommend below stats to make it all a bit easier.
40+ for Rune weapons
55+ for Helm of neitiznot and Rune armour
50+ for Iban's staff
50+ for Magic shortbow
43+ for Overheads
All Slayer masters are located directly east of the bank at home except for Konar who is at Mount Karuulm at the Brimstone chest. I will only list the masters I have experience with.
He is your best friend up until 95 Slayer. You can 'Talk to' him and select 'Can you skip my current task for a easier one please?' in order to replace your current task with something super easy like killing cows or rats. This will be very useful when you are getting your Slayer level up because you can just task that are either too tedious, too long or too difficult for your current Slayer level or equipment.
Classic wilderness slayer. All tasks will be in the wilderness and you can get killed by other players. But you have the chance of getting a key to the Larran's chest which can be very profitable. In addition to that you can get emblems you can either sell or trade in for Bounty points and buy gear with it in the shop.
Konar quo Maten
This Slayer master is for tasks that will be locked to a specific area. You will have a chance of getting a brimstone key in order to open the brimstone chest. (Note: Some tasks are bugged at the moment and may not be able to be completed in the area assigned. Just skip with Turael in that case)
This is probably the only Slayer master you need from level 1 to 99 if you exclude skipping with Turael. You can get easy, medium, normal, hard and boss tasks from him.
They each have a Slayer level restriction:
Easy: Can be done at Level 1
Medium: Requires 40+ Slayer
Normal: Requires 70+ Slayer
Hard: Requires 75+ Slayer
Boss: Requires 95+ Slayer
The simplest way to get to 99 Slayer is to just head to Steve for tasks and pick the highest one available. If a task appears to be too difficult for you at the moment and you struggle with it just head to Turael and skip it with an easier task. If you want you can spice it up a little by throwing in a Krystilia or Konar task when it is getting to boring for you but that's generally a very good strategy.
You can kill cave horrors after you have 58 Slayer for a black masks which is highly recommend to wear at all times (if no other headgear is required). You can later unlock the Slayer helmet for 400 slayer points.
Once you hit 75+ Slayer you can also start killing Gargoyles for money and some supplies. It was worth it for me and it may be for you.