Typically, every month there is a new Battle Pass. This is a set of events that will lead to specific rewards. Every day, you'll be required to do some events to get tokens to progress on the battle pass.
Each day there is an event that will reward a certain number of points that count towards your progress. There are many different events, so typically there is:
If you click on an event, you can see how many points you need to get there.
Once you complete an event, you can collect the rewards up to that point. Each reward has a certain number of points that you need to get to it. To just complete the battle pass, you don't need to do all the events, but you should because there is another event that gives nice rewards if you finish every single one, the Heroic BP Overflow Event.
This event gives you a lot of recruit tokens, and usually gives you some shards whatever officers are being introduced this month. In addition, you get broken desealing rods which will help you to open your latinum vault after 12 pulls (or 6 pulls of this and 6 of monthly chests).
During the battle pass, you will often have events to help you recruit the new officers being introduced that month. These tend to be challenging and require you to have certain resources and tokens saved in order to do them. So what are the typical events?
This event requires you to spend a certain amount of grade 3 uncommon or better resources. It often has a rather high goal, so you need to be sure you'll have enough saved each time. So you should never use these resources outside of these events if you can avoid it. This event is both an SMS and SLB, with the SLB usually giving you a full unlock if you win, and some amount of the officer shards if you don't.
Exactly like the uncommon spend, except you have to spend Ultra Tokens. There is an SMS and SLB and this usually goes towards a full unlock as well.
This event also often happens during a battle pass. You'd have to spend directives to succeed at it, usually two rare and an epic, or three rare plus a few joined. To make sure you have enough Rare and Epic directives, make sure you are doing this event properly: Crucible of War
A story arc is a group of battle passes that tell a longer story. This can last anywhere from two to four battle passes.
At the end of a story arc, you will get an event store. In the event store, you will be able to buy tons of different things, including some things that are almost impossible to get elsewhere. So what to buy? The following are quite good if available
As tempting as it is to buy other ships, it's usually not worth it. The blueprints for the ships available in the faction stores will come with time, and these can only be gotten here in many cases, or in rare events. So it is better not to spend on them.
You can also buy officer shards, but again they are often overpriced. From officer shards, there is often a pack of officers from the current arc. The price there tends to be quite good, so that is very much worth buying. In addition, some of the rarer officers are also quite good to get if you have some credits to spare and they happen to be there (depends from arc to arc).
Otherwise it's at your discretion, but often it's only worth it if you need a couple shards to get the next tier.