Hi Jim, and welcome to WW.
That company isn't actually a publisher - as in, a company which will pay you for the right to publish your book, publish it at their own expense, and then recoup what they've spent through sales, and give you royalties. You can find those in the Writer's and Artist's Yearbook, and if you're writing fiction and hoping to approach most of the imprints of the "big five" mainstream publishers, then you'll need an agent.
The one you mention is a self-publishing service company, where you
to help you put your book into book form and get it out there. That's a perfectly legitimate business, although their list of authors is very short, and I wouldn't myself trust a company that had so little experience. There are bigger and more established companies around, which are listed in the bible of all these things, the Writer's And Artist's Yearbook. It also has loads of good advice, as well as listings.
As I'm sure you know, there are vanity publishers out there, although they never
call themselves that - sometimes calling themselves "subsidy publishers" or "co-operative publishers". They pretend to be actual publishers (unlike these guys, who are being perfectly up-front and honest about being a self-publishing service company), are hugely flattering about your work, talk about how they're happy to take risks on wonderful new work, unlike mainstream publishers, how your "royalty" will be much higher, etc. etc., But actually they take on anyone, because they make their money out of authors, and have no incentive to push your book. A friend of mine photocopied a washing-machine manual and sent it to one of the huge US companies, and got just such a letter back!
Edited by EmmaD at 11:37:00 on 06 June 2015