what libraries and which objects in them do you find essential?

Libraries are collections of objects for PD. The original PD Vanilla, written and maintained by Miller, has a limited range of objects, but as it is open source, there is nothing stopping other people writing new objects for more specific needs. Some of these objects are just PD patches themselves, which you can open up and see how they run (see list-abs for example). Others are written in external languages like C. These are called "externals".

Projects like PD Extended have large collections Libraries built into them already, so if you have PD Extended, you can go to the PD Help Browser to see which libraries you have. If you have PD Vanilla, you'll need to download and install libraries yourself (a plugin called "Deken" is supposed to be good for this, although I haven't tried it myself).

Everyone will have a different answer for which libraries are essential, but personally I use zexy, list-abs and iemguts very frequently.

I'm a pd noob so it will probably change, but right now, cyclone and list-abs are saving me a hell of a lot of time. I think i'll probably be using Zexy a lot as well. With the zl object and list-abs you have power like a fiery regEx jesus