I am interested in finding a few good book publishers that encourage new authors to publish .

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Amazon.com can publish your book on an "as needed" basis.

There is no simple answer to that question - no special list for first time authors. You have to advocate for yourself and put in the leg work like everyone else. And those willing to do the work have the best shot. Go to the library and use Literary Marketplace - the Author's Bible. Search for publishers who are currently reading work in your genre. Make sure you apply to them in the correct format - following submission guidelines to the letter. When one rejects you, try another. It is not an easy thing. Nothing is going to happen overnight. There are no magical secrets. It is all about how good your query letter and synopsis are so that it attracts attention. If it doesn't, it heads to the slushroom for rejection. The best shot you have is learning how to write an outstanding query letter and having a great book that reads well in synopsis form. And you need to develop a skin thicker than steel belted radials because you will need it. Rejection comes with the territory. Hope that helps. Pax-C

Lulu.com is a website that publishes books online by unknown authors and other people go on and buy them, its for all ages so I recommend it. Its not specifically first time authors, but it would work.