Which of the below ways are best to monetize my side project?

Oh awesome! Glad you decided to just ship it. :)

What's your tech stack? No code too? It looks great - clean, minimal and easy to read.

I wouldn't pretend to know the answers to your questions. They are stuff that I'm also in process of figuring out. Some early thoughts I have:

How narrow your niche and location of jobs depends on how much you know your target customers. I think it's always better to start with the users you know really well, then expand from there as more people use your product. I started with design+gov jobs, as that's the field I'm working in and most familiar with.

Pre-vetting candidates sounds like the job board is moving into the work of recruiters and talent search agencies. It does take quite some work, and you need to work closely with the employer to understand the profiles they are looking for. For me, that feels like something of a later stage development (if ever), after I validated that there's a demand for the job board and engaged employers enough to understand if they need that.

Packages is tricky. I like the simplicity and low barrier of a one-time fee for a job post for job boards as a starting point. Because employers often hire varied positions across the board, and only an occasional data viz guy perhaps. So to ask for lifetime package might not be what they really need. It makes more sense for more general job aggregators like Indeed/Ziprecruiter probably. For me, until employers start telling me otherwise, I'll stick with $99.

I'm posting for free now at the start, so that I can grow the job board to look more substantial, get more traffic and people interested. In time, when there's enough traffic and captive audience, the fee will be worth paying for. But that said, your ad banners and resume services sound plausible too.