My favorite quick reference I have printed out is
http://clqr.boundp.org/ It's nice to just quickly explore what's available in the base language too.
But when I don't want to flip through it, or find the short description for something insufficient, then yeah the HyperSpec is usually my first stop for quickly referencing something. I use vim, so I just move my cursor over a symbol and type ",h" and that opens a browser tab on that thing in the hyperspec -- e.g. if I want to remind myself what the state parameter of make-random-state does, I open http://www.lispworks.com/documentation/HyperSpec/Body/f_mk_r... Though I often first type ",s" which is just an alias for (describe 'symbol) which shows me locally the symbol documentation, and for this one I'd learn the same thing without having to have my browser open. I think some people configure their emacs to do the common IDE thing of showing you the doc along with the function signature as you type, I just have the latter. I also make use of jump-to-source since reading the code is often the quickest way of answering a question about it.
PAIP is a great book, but I tend to use PCL as a quick reference: https://gigamonkeys.com/book/ Especially until you use classes/format/conditions/loop enough to get used to them, chapters 17/18/19/22 are helpful. It's still a recommended first book for newcomers that's worth going through entirely though, not just as a reference.
https://lispcookbook.github.io/cl-cookbook/ is a useful community cookbook with info on a lot of topics.
CLTL2 is a reference I haven't used that much, there are a few things that are in it that didn't make it to the ANSI spec, but what I have read I've found useful and clarifying. https://www.cs.cmu.edu/Groups/AI/html/cltl/clm/node1.html Guy Steele (whose 67th birthday is today) is a great writer.