Depth is something that will allow you access to different areas and stages of the game, the latest patch (1.69 as of now) brings new NPC changes which makes getting depth a little easier.
First of all, most likely, you've just finished story, the traditional route is to farm PT and sit around at 168 depth because you didn't know that Third World gives accessories.
COUGHThey give accessories COUGH.
You'll have to complete the first 4 or so-ish to reach the accessories that aren't lower than 90 depth. The quicker route is now to buy stuff from
Vice (The guy sitting around near a globe)
What does he sell? Equipment. Better than your ones that are freshly out of story. Price range each varies from 5k to 6k because you're only buying the ones at the very end of the second page (Don't have to buy all of them).
Then after doing so you go and do some Player Training with a little bit of Third World to get those accessories the same depth as your equipment (If needed).
This is what I found easiest to do, I did 3 Player Trainings and completed all my Third Worlds, this may vary from characters as I did this on Izanami, on others you may have to try harder because Izanami is a bit more stronger than the rest of the Heroes as of 1.69.
Doesn't mean it's impossible however. If you can't complete them then perhaps ask for help but you can only duo once you reach the homeless dude with a beanie.
After a little effort you should be at Liberation, if you're not then find your lowest depth equipment piece and farm PT for it. Now, after pressing the tab of 'Liberation' you'll be introduced to some dialogue and at the bottom right a new place will be unlocked 'Liberation Wing'.
If you have any of those Rose Fragments then buy those gear from Rose, the NPC on the Right-ish. If you've farmed enough Nightmares then she should give you 140 depth, if not, settle with the rare gear. The gear is good for some depth boosting.
Ali Baba (Smug af)
He'll give you some mysterious items that costs 20k coins, 600 Maya Fragments and 4 Epic coins. You get Mayas and Epic coins from dismantling equipment, Epic equipment give epic coins ;D.
You don't have to get them all. It'll be easier but you probably wont have enough pennies or epic coins. Buy a necklace or any accessory as those will probably be lower than your actual equipment + anything else and when you go to do liberation the items will scale up. So if your gear is at 93 depth then at the lowest (+ Unluckiest) it'll get scaled up to 100 if Ali here doesn't scam you. Doing a few liberation you can easily get to 2xx depth at level 9x or 10x
If you don't want to buy from Ali boy you can do some Labyrinths and some Liberations normally but remember to balance them out so you don't get held back from either lack of depth from your equipment or your accessories.
After that it's Hard Liberation at 190 Depth, you just farm from here. 145 is the equipment cap + Accessory cap. Then you have to farm mods ^v^
Unfortunately I've only done this once with Izanami so make sure you have enough pennies and Fragments to do this. After this you'll hit Third World EX and best wishes from there.
Make sure to get your best suited mods and a clock to help you through. Or an EX carry *Wink*
It'll probably be better to also consider the Sidekicks you're using, if you can't complete Third Worlds or EX and maybe Liberations + Labyrinths.
I would suggest getting Lote, Abel, perhaps Myriad if you're having health issues and Saravati to superior. But some characters vary on which Sidekicks they use.
The one I use is purely for some damage and a heal + stun from Saravati.
ALL of this is OPTIONAL of course. You don't have to but it'll be quicker if you buy a few items, even one, and do some PTs or Libs. Then the equipment will scale up.
I'm a noob, it's best to experience the game for yourself and spend how you wish to.