What are 3 of the most accessible self-publishing companies for authors ?

If I personally had to pick three self-publishing companies to publish with, I'd go for Amazon, Kobo, and Smashwords.

Asking that won't help if they don't publish the genre you're writing. 

You can publish immediately and free on Amazon including print on demand paperbacks.

Draft2Digital will post your book on multiple retailers.

If you just want personal copies, a vanity press will do it for a fee.