KDP (Kindle Direct Publishing) is the easy way, but not always the best way, to distribute your book. KDP is a POD distributor, so you just upload PDFs of your interior and cover using their specifications. There is no upfront distribution fee. They’ll let you review your layout electronically. You can upload corrected versions as many times as you like for free. Your book will be sold only on Amazon unless you opt for expanded distribution, which will cause Amazon to take a bigger cut from your retail price. From what I’ve read, expanded distribution is not as good with Amazon as with other distributors. But if you are happy with Amazon as your sole bookseller (and you can still sell author copies yourself), it’s a good distribution deal. And KDP is a great place to publish ebooks, since Kindle is such a popular e-reader.
As for printing, I have found Amazon’s printing to be just fine (not substandard). They use 50# paper for black and white, and I haven’t had any problems with bleed-through; clarity of print seems to be fine. They do have only one expensive option for color printing, though, so be aware that you may be able to get color printing more cheaply elsewhere. They insist on using slightly thicker 70# “premium” paper with no other options. I saw a difference in texture, but it didn’t seem worth it to me compared to printing color on regular 50# paper.
PS: You can also submit your book to more than one printing/distribution company. Here’s an article on the advantages of submitting to Amazon KDP and Ingram Spark for the same book.