Let It Die

If you think you even might play the game at some point, I'd suggest loading it up and create your account, etc. There are events that take place over time and they reward everyone with an account made before certain dates. As it's a F2P game you want to have as much free premium currency coming your way as possible.
On a similar note, if you have PS+ there is a one-time free pack you can purchase/download which gives you some decent items but also more free premium currency. More than enough to help you get started. If you want, there is a further one-time IAP currency package you can buy for roughly $5 which provides a lot of bang for your buck.
That said, so far there's no real need to worry about the necessity of IAP. The game plays fine without investing a cent.
As a last tip for those "just setting up an account" for later, while there is a multiplayer raid system ("Tokyo Death Metro") which you can run afoul of (and to which two of the three currencies can be stolen from you), you have to get through the first three levels and the first miniboss before it unlocks. Even then, it's technically optional to opt-in when it does.
The three currencies from most precious to least are Death Metals (rainbow skulls), SPLithium (blue and white flame) and Kill Coins (gold coins). You can periodically get DMs through daily login bonuses, etc. but generally they are the purchased IAP. They can be used to continue without penalty when you die, or used to expand your storage box in your Waiting Room (home base between runs). I would tend to recommend using them for the latter at first. SPL is generally found from beating particularly difficult special enemies, or by different forms of raiding, and it's mostly used in large quantities to upgrade your Waiting Room (after TDM unlocks) or else small quantities to research Blueprints that let you purchase your own weapons/armor. Kill Coins are what you get as drops and also from selling gear, used to buy Decals (equipment perks), your Blueprinted gear or else to use the elevator to get to and from the Waiting Room and different floors quickly.
Your overall account remembers weapon masteries and controls overall currency and storage items. Your avatars (Fighters) can be destroyed and lose Decals and carried equipment, but you can always make some progress.
Weapons you find early on are very low durability and tend to break at the worst moments. Start by using your fists (in a basic LRL or RLR combo) instead. Weapons "level up" when they actually kill enemies and every level has its own perk. Eventually (Level 5 Mastery) you will get a special heavy attack move for the fists which makes the game much easier at the beginning. Wait until you get blueprints to focus on any other weapons.
Your best healing items at the beginning are (cooked) frogs. Always keep a firework gun (fairly commonly found) on hand as locking onto and shooting frogs cooks them immediately in the field.
Magnum revolvers are really handy for those "particularly difficult special enemies", especially those apparently much higher level than you. Rare, but worth keeping one on hand as well.
Blueprints only start showing up on the second floor or higher. Get them back to your Waiting Room at all costs, as well as the raw materials needed to make them work for you.
Elevators only have stops at floors that are on the same vertical line as the floors appear in the overall floorplan. Bear that in mind when trying to get back safe with your loot.
Eventually you will want to unlock and activate the TDM to progress (as it allows you to increase your Fighter count, KC/SPL bank size, and levels/types your Fighters can be). Take your time getting there and maxing out the levels on two or three Fighters first. Once you activate TDM, keep your non-DM currency counts low, tied up in stored items or else rewards in the reward box until you actually need them so they can't be raided.