Depending on the size of the PE part, where and what it will be glued to, you will want to have several types of glues on hand. Along with CA glue, both thick and thin, slow and fast setting, have CA accelerator on hand as well.
I also will use epoxies, white and clear glues, caulk, silicone, clear gloss enamels right from the bottle and tacky glues. I have even used future. You will find with PE that no one glue does it all.
Glue is not the only way to affix PE. I have made holding tabs with styrene to hold PE parts. I have also cut groves and slots to hold PE.
Not all PE parts are better then the plastic part it may be replacing so check both options to see which you like better. I have also used the PE part or the fret it was cut out of as a template to make a better part with styrene.
You can scan your PE sheet into your computer and print paper templates to cut parts from styrene. You can also use the scan to print on clear plastic sheet to make parts. Have fun with it and think outside the box.
Don't throw away left over parts or the fret. You can use the parts for other builds and you can cut the fret with scissors to make straps, seat belts, tie downs and more.