That is the question. Unfortunately, the answer is anything but simple.

Publishing your book through a Print On Demand publisher is a sure-fire method of seeing your book in print. Some do an excellent job and some do a terrible job. The challenge is to find a reputable opinion. 

Fortunately, there are souces, individuals and blogs that will give an unvarnished opinion. And, there are "blogs" that seem to sing the praises of only one POD publisher. Run, do not walk, from such a publisher. 

One blog I have found consistently on the truth is at Writer Beware.com. I have no connection with Writer Beware other than being a reader. But, I find them to be very believable.

And of course, personal recommendation is a usually reliable method of selecting a POD publisher. 

Occasionally, a reputable magazine will survey the POD market. They rely mostly on the experienced of those who have gone before you. And, opinons will vary, but usually the bad apples smell bad enough to warn you away. 

PODs rarely put forth much effort to market your book, so no matter who you pick, unless you are willing to spend big bucks, the marketing effort is up to you.