@Janette is your client a member of SCBWI? They have great resources for self-publishers, including webinars and The Book. SCBWI-Michigan (my regional chapter) has indie advisors (I volunteer as the PB indie advisor) to help self-publishing authors through the process.
On the printers others have mentioned, I’ve worked with both in the past (just did book design for a client using KDP and Ingram Spark, in fact).
Ingram Spark — they do print a landscape 11 x 8.5 in hardcover but there are limitations with that trim size. Their printing can be hit or miss — that has to do with a couple factors: print options that have been chosen and they have several printers they work with so there’s no guarantee where your book will be printed and at times quality control is spotty. If your client chooses to go with Ingram Spark, they should choose the premium color option for best color printing, even though it will cost between $8-$9 per book, plus shipping.
Lulu — I worked with them years ago and don’t recommend them. Granted, they could have improved their printing and customer service, but from what I’ve heard, they’re still sub-par in terms of going the print-on-demand route.
While I haven’t worked with Print Ninja and haven’t seen samples of their printing quality, I have gotten a quote from them and printing a hardcover book is quite expensive, one of the most expensive per-unit prices for a US-based printer.
The other thing to mention if your client is going to go the print-on-demand route: it will affect the book’s layout so plan accordingly. Most POD companies require that the last page of the book be kept blank for their use, so if you’re going to print a 32 page book, you would actually upload an interior book file with 31 pages of content. This will prevent any additional blank pages from being added to the book.
Hope this helps. Let me know if you have any other questions. 😂