What kind of glue should I use to create a perfect bound paperback?
There are machines for doing perfect binding on a small scale.  They start in roughly the $50-$100 price range, and go up from there.  They're generally "thermal" (they heat a strip of hot melt glue in the binding).  If you search "thermal binder", you'll find a bunch of options.  Here's a random, low-cost example from Amazon just as an illustration:


Source

Most of the large companies that make binding equipment and supplies, like Fellowes and GBC, offer versions.

The general way they work is you use a cover that has a glue strip in it.  You wrap the cover around the pages and stick the assembly in an upright guide over a heating element.  The machine melts the adhesive, then you stick the book in a cooling stand.  The whole process takes a few minutes per book.

You can buy premade covers that have an opaque back and transparent front, so your own cover art shows through.  They also sell glue strips that you can stick in your own cover.

I've used similar machines that were more "commercial grade".  The process is simple, fast, and clean, and the results look very professional.  They work with any type of paper and don't affect the printing (the heat is applied only to the edge).  

If you mess up, or need to remove or replace a page, you can usually just put the book back in the machine, remelt the glue, and swap out the page.