It's definitely something your developers should do, although I would give setting up the logs to a more senior developer, as you need to know what stuff are useful logs and what are not.
In any way, logging is one of the things that needs to be done in iterations, so you make the basic setup, then observe for a while, then tweak it later on to increase the useful logs and remove the useless ones, and so on, until you get what you need.
What I have learned through several years of experience, is that by default you should consider SQL database (like PostgreSQL, MySQL, ...) and if does not suit you then you should explore other noSQL options.
SQL is very solid and it can do almost anything and can support almost any kind of systems.
So, for your case I would recommend that you go with SQL. You should start by listing your use cases and infer from them your entities and relations, and work on them in a Top-to-bottom manner, meaning that you should have some entities that are the core dependencies for the other entities. Or, in other words, they can exist without other entities existing, but the opposite is not true, these are your core entities that you should work on first, then gradually build the other entities.
One way to figure out the core entities is to follow how the users will behave in your system, what will the user create first, and what is dependant on other entities.
For example, in your case, on way to do it is to start with the "vault", as everything else cannot exist without it (and it's the first thing a user would create), then do passwords as they depend on the vaults (I would say passwords are "under" the vault), then once you do them, you can start working on tags then categories, and so on...
