Opt In first time

Hello, I am new to placing an opt in option for my website. I have seen plenty of plugins for opt in options. My question: I hear people say that you must select an email provider to have an opt in option for potential clients. I am a little confused because I already have an email provider through hostgator, gmail etc. What is the difference with having an email provider for opt in options vs my general email providers. And is there a way to pick a plugin that with show me a list to who is subscribing, that way I can copy that list my personal email providers.

Also, I am a little confused on picking a contact form. Can someone break down the contact form as it relates to creating opt in options. Just trying to understand the technical concepts of this all. I understand the fundamentals. (i think)

And is there a way I can create a button once a potential client hits subscribe that will take them to a page that will give clients their treats (downloads, videos, free tutorials) once he or she opts in?