@PotomacBobThe publisher is responsible for every aspect of getting your book into print. This includes editing, cover design, marketing, printing, arranging contracts, and so on. They handle all financial and PR aspects. The may have an in-house printer or use whatever is available.
The only thing you (may) need to do is get an agent before talking to the publisher. Even that will vary. In some cases a publisher may help you arrange an agent, but this usually only happens if your text is sold gold and the publisher snaps it up quickly. Most new authors get an agent who helps them make the manuscript more attractive to publishers.
All a printer does is actually put the text into physical form. If using a printer without having a publisher you are self-publishing. This means you have to arrange all the details yourself including paying the printer upfront for the printing cost. Once you have the physical copies you then need to figure out how to sell them.
Publishers often have contracts where they control the copyright for a set number of years before rights revert to you. This is normal and it is your agent's job to help you get a good deal. Ultimately, most new authors don't break even on sales of their first book; publishers are investing in authors hoping that later books will take off, thus increasing sales of early books. This is why they need to hold copyright for a certain time, so they can capitalise on early books later if you take off.
If a printer wants copyright in any form or for any length of time, it's a scam. Do not sign anything with them. A printer is providing a service only, they are not involved with the product.
Note that under the Berne Convention the author automatically has copyright as soon as the work is completed, but in many countries it is necessary to register the work in order to protect it legally. In the US, for example, you cannot sue someone for infringement unless the work was registered prior to the lawsuit (or possibly before infringement, not certain).