Obtaining a balance between mass mailing versus spam protection is a very, very delicate and complicated thing. It cannot be described in a simple answer. It's an art by itself :)
Whatever means most is so called "reputation" of the sending site. This is very vaguely defined and every mail recipient has their own definition :). If the site does not send unsolicited emails (ie. all newsletters/mailings that it sends are truly opt-in), there are few users' complaints to ISPs about the messages they receive, the site does not start sending thousands of messages suddenly, but builds its email presence slowly and consequently (it's so called "warming up" of the sending server), and of course has everything properly configured (forward/reverse DNS, SPF, DKIM, DMARC) - it is generally considered "trusted".
If you really want to learn these things, the best option for you is to subscribe to "mailop" mailing list: https://www.mailop.org/ and browse the list archives. It's a topic continually discussed on that list and there are people on that list who are professionally working only on that.
Of course you can ask the people on the list your questions, but I suggest reading the archives first to understand the scale of the problem. It is fairly non-trivial.
If you don't want to do this yourself, you can use some service that specializes in mass mailings like Sendgrid (Sendgrid actually is not a very good choice now as there is more and more spam coming from Sendgrid and some recipients decided to started blocking it - previously it was considered a reputable sender, so you can see that everything constantly changes in this field; but there are other similar companies like the ones you mentioned). They all provide instructions on how to use them.