I get this question a lot-- got it again today, which is what prompted me to start this thread.
People often write and say, "Okay, I get it-- PublishAmerica's no good. But then what publishers are good for new authors?"
The same ones that are good for "old" authors.
Please take this to heart: If you want your book to be read by strangers across the nation, then it needs to be published by a publisher who can actually get it into bookstores.
How will you know who those publishers are?
Simple: Go to bookstores.
If you're writing a mystery, visit the mystery section. If you're writing a self-help book, visit the self-help section. Open the books. See who publishes them. Check the acknowledgments to see if the author thanked the editor-- probably did, which gives you a contact name. Check if the author thanked the agent-- if so, that tells you that the agent is capable of getting books sold to publishers who can get books onto bookstore shelves. Write these things down. Then investigate at home.
Visit the websites of the publishers you found. See if there are writers' guidelines on the site. Usually are, but sometimes you have to look around-- under "contact us" or "about us," often. There, you'll find out what the publisher wants and how they want it. Follow the guidelines. If they ask for queries only, then send a query. If they ask for snail mail, send snail mail. If they ask for a few sample chapters, send them. Don't send more than they ask for. Don't bother with FedEx and signatures and whatnot... regular 1st class mail or Priority Mail is fine. Some publishers will accept queries or proposals by e-mail, but don't get lazy-- don't restrict yourself based on who accepts e-mail submissions. Most of the better houses still expect snail mail.
(And the better houses do NOT advertise for new authors by Google Ads, or in the backs of magazines, or on the front page of their site. They're inundated with submissions already, so they save their ad dollars and prime publicity spots for the books they've published-- that's what brings them money. Vanity presses make their money from new writers-- which is why they advertise for them!)
You can go either way or both at once: Contact agents first, publishers first, or both at the same time. Presumably, as a new writer, you'd like an agent-- you don't know what to look for in a book contract or what's reasonable to expect, so an agent can be very helpful. To find agents, subscribe to PublishersLunch and see who's making deals (http://www.publishersmarketplace.com/lunch/free/).
But in short, there's no handful of "good publishers for new writers." "New writers" isn't a genre. All publishers are looking for new writers. You just have to be good enough that you don't come across like a new writer. That is, no publisher is going to take pity on you and lower their standards because you're new. Your writing has to compete with what's already out there, which means you need to feel confident that you've worked on your craft enough to deserve a spot on strangers' bookshelves.
I'd be very wary of publishers specifically advertising that they specialize in new authors. Normally, this means either vanity publishing (you pay to be published), or a new and clueless publisher with stars in their eyes and good intentions, but no distribution.
Some legit publishers will accept agented submissions only-- or at least they say so. (I've usually found that a strong query letter will get you in the door no matter what the usual policy is.) Others will accept queries from unagented writers; others will accept sample chapters or even full manuscripts unsolicited. Look around. Read guidelines. This isn't the time to skimp on research or to rush. You spent the time writing the book, now spend the time to find it a proper home.
As a supplement to your own research efforts, you can use Writer's Market (an annual book published by Writer's Digest) or the online version. In it, you'll find contact info and guidelines for tons of publishers, large and small.
The key to knowing whether or not a publisher can do anything for you is whether or not you can find that publisher's books easily in places where books are sold. If you can't, think hard-- is that what you want for your book? If the publisher can't get your book into stores, then sales will primarily go to your friends and family. Don't be impressed by the fact that a publisher gets books onto Amazon and BN.com. Anyone can do that, and it doesn't mean anything. Readers don't run around Amazon searching for authors they've never heard of and books they've never seen. If they do go looking for someone on Amazon, it's probably because they heard about a book from someone who bought it in a bookstore (or Walmart, Costco, CVS...).
Two, five, or twelve rejections means nothing. Don't lower your standards, just as you wouldn't expect a publisher to lower theirs. If you've received dozens of rejections, take a hard look at your manuscript again and consider revising it. While you're submitting your work, get to work on another book. As hard as it is to hear, often, writers' first books aren't meant to be published. They're meant to be practice. The second or third book may be the charm.
In short, don't go looking for "good publishers for new authors." Look for good publishers for authors, period. Real, reputable publishers buy the work of new writers EVERY DAY. Ask dragonjax, who just sold a 3-book series to Kensington yesterday... her first book.
Anything that looks easy, looks like a shortcut, looks like a back door into publishing... probably isn't where you want to be. You may get some temporary satisfaction from easy acceptance, but in the long run, you'll be miserable that you allowed your book to receive shoddy treatment and doomed it to your basement. Hold out. Keep working. Keep submitting. It's worth it.