Getting through Canto II is important because you unlock Mirror Dungeon which is the best way to get yourself currency through the Battle Pass. Mirror Dungeon gives you Battle Pass levels and you get 3 weekly bonuses to it which give you lunacy and increased Battle Pass experience, you can do as little as 1 run a week when you unlock Hard Mode. If you do plan on getting the Battle Pass and playing for more than one season purchase a Lunacy pack rather than the one made for the Battle Pass since you'll save money in the long run, the game is still very F2P friendly if you don't but its not as generous with your yellow crates. Just don't use the paid currency on pulling unless its for a daily pull (13 lunacy), but stay above an increment of 1300 (1300,2600,3900,etc) since that will cover the next seasons BP.
You're also going to need Modules from Enkephalin in the long run so its a good idea to keep on top of converting them. For recharging 1 unit takes 6 minutes so that's 10 units an hour. Usually I just launch the game on my phone in the morning to convert, go about my day and then by the time I actually play I have enough Enk to do story stuff if I needed to. Generally don't use skip on Exp and Thread Lux unless you absolutely need it or have have a massive stash of modules. Thread Lux costs 2, Exp Lux costs 2 or 3 when you get the better ones, Mirror Dungeons is going to eat them up with taking 18 to get your weekly bonus (it costs 5 without to get 3 Battle Pass levels on completion), Refraction Railway (endgame content) will cost 25 to unlock the rewards. You can get away with doing 1 Lux a day and ignoring the bonuses on thread lux since they're marginal in the long run compared to module cost. Doing a daily refill of Enk is also very economical since it costs 26 lunacy to add your entire cap on top of what you have (ex- you're at 60/120 it will give you 160 and you'll be sitting at 180), you get minimum 1050 lunacy a week (300 regular maint, 750 all mirror dungeon bonus) and it only costs 182 if you do 1 refill a day. I'll talk more about Thread a little later.
With Pulling/Rolling for IDs it gets a bit divisive for early game. You have a strong starting line up and you'll really only start having trouble around Canto 5 (The Evil Defining) and I would recommend saving your Lunacy and Extraction tickets until then, if you get a guaranteed extraction ticket just use it since it helps fill out your roster. There's a special banner that's supposed to happen quarterly called Walpurgis Night that has limited IDs and EGO you can only extract during that time, or dispense the previous banners contents while it is running. This is what most people save for since the units are generally stronger than regular releases. You also end up with a lot of Shards which are used to freely dispense IDs and EGO from the shop or upgrade the ones you currently have. You earn shards from getting duplicate IDs when pulling, opening red crates will give you 1-3 random shards, and opening yellow crates gives you 1-3 of your sinner of choice. You can dispense from any season but the one directly before the one we're currently on, since we're on Season 5 you can't dispense Season 4 until Season 6. With shards and Yellow Crates you can effectively eliminate the need for Lunacy outside of WN (you can also just wait until the next one to dispense the previous IDs/EGO) and build up a massive stock to guarantee yourself everything. 2* IDs cost 150 shards, 3* and EGO are 400. The next one will be within 2 months so you could easily save until then with your current roster + your season 2 pick.
Getting Yellow Crates is the issue. You get them from Events and as rewards on your BP. If you max out your BP (120) you will earn 1 per level on your BP and if you've purchased the BP you earn a bonus 2 per level as a paid reward. Using the weekly bonuses you get more BP exp from MD, but if you run MD after you've used your bonuses you only get 3 levels and it takes about 30-40 minutes. So you can earn 3(free) or 9(paid) per run of MD, which will give you between 3-9 or 9-27 shards for your desired sinner. On average you're going to end up somewhere in the middle when you open them though, sometimes its a little more or less but again that's the average. So if you were saving for a 3* ID and you were starting at 0 shards you would open 200 yellow crates.
To circumvent no one having to put any money into the game your crates and shards get halved at the end of the season and turned into thread. Crates turn into thread crates that give you 1-3 and shards are directly converted to thread. This is also why you can get away with doing a single thread lux.