Recs.
Updated
Spac(emacs) with pdf-tools has convenient default keyboard shortcuts (e.g. vim-style with spacemacs) and has potentially the best annotation support, as combined with the org-noter (or interleave) package annotations are automatically exported to a notes file and backlinked. Through spacemacs, pdf-tools is easily installed and configured. Because it is an emacs package, the reader is ultimately configurable and hackable.
Specs
Pros
Cons
Con Too cumbersome for quick reading or annotating
Although setting up pdf-tools is not too much work. For quick reading using some default pdf-viewer like evince/okular/zathura is recommended. Also, except for the auto-export feature (with org-noter/interleave package), other editors like e.g. pdf-XChange Editor (via wine), Okular or mupdf have even more powerful annotation features.