For me, the essentials are the Core Rules, APG and the Bestiary. I got by for a while without the latter - having been a 3.5 GM for a long time and having the Monster Manual, supplemented by the SRD. However, having the Bestiary itself proved really useful in-game.
I own UM which in my view is excellent, but not essential. I haven't picked up UC (on principle - Guns...uuugh! - I'm a dinosaur that way) but I suppose I would if any of my players got serious about playing a Monk. I also love the Inner Sea Guide which you already have, and I love that too.
I would echo others' comments about the GMG - not essential but by a distance the best GM guide I've ever seen - the towns and NPC sections in particular, but tons of other great ideas as well.
The
Pathfinder SRD can get you through a lot of "one off" occurences of mobs, rules etc.
If you already have the Core Rules, APG and Bestiary, I would encourage you to look at
Hero Lab - for me this is the next "essential" as it so totally streamlines the PC creation/development process. I can't begin to estimate the amount of time this has saved me, not to mention the number of errors I would probably have made in trying to remember every single variable. I can see it would tend to restrict which rule sets you use - if you are into a lot of third-party content for example - but I'm not, and all the core stuff is there (including for example AP-specific content). Hero Lab costs money - with datasets for my books I've probably spent the same as two rulebooks - but to me that's still good value.
I also really like
Combat Manager - in addition to auto-managing many aspects of combat (for example easy management of initiative fluctuations) it has good databases of rules, spells, monsters etc which can really save you time. It can be a little bit flaky in terms of rendering screens and the occasional crash (on my netbook) but nothing really to worry about. And it's donation-ware.
In play, I run Hero Lab, Combat Manager and
Evernote (for general campaign logging, keeping track of magic items as-yet-unidentified, etc). My players tend to hog the Core, APG and UM books (and when they get their hands on it, the Bestiary). Inner Sea guide and GMG are much more situational.
Hope that helps
~ST.