See if I were starting a new website today, I'd get things moving pretty quickly.
But I wouldn't start buying backlinks right away.
First, I'd spend the initial 4 weeks getting the website properly set up and warmed up.
I'd publish 2-3 articles every week. That's the first thing I'd focus on.
By the second week, I'd also have all my social media pages created and ready.
Once the first 4 weeks are over, I'd go for a press release.
And then comes the interesting part!
I'd start searching for my target keywords on Google every single day.
Open the results, read the articles, explore the websites and see where I can leave comments.
If I find a relevant discussion, I'd leave a comment.
If there's an opportunity to make a post on a website, even better!
I do this myself, so my comments are always genuine and actually add something to the discussion.
Now, if you can spare 2-3 hours daily for this, you can easily get 2-8 links on most days.
Some days you'll find more opportunities, some days less.
But there are plenty of opportunities if you actually spend time looking for them.
Once you've built a few links yourself, I'd say it's time to start buying guest posts.
Now, coming to your main question about which types of backlinks work.
Don't get too caught up trying to figure out which ONE type of backlink works best.
A website that's actually growing will naturally get links from all kinds of websites.
I'd slowly work on building different types of backlinks.
Once again, just check the top 100 Google results for all your target keywords and see what kinds of links those websites have.
Try to build different types of links accordingly.
If you ask me what I'd continue doing every month, guest posts would be my main focus.
Keep getting guest posts every month, build different types of links along the way, and you are good to go.
That's pretty much it!
Hope it helps.