This is the screen protector I bought. I'm very happy with it, the installation was incredibly easy (never again am I buying a flimsy screen protector if a glass one is available!), my only tiny bubble at the corner disappeared after about a week, and the glass is much more pleasant to the touch than plastic screen protectors.
I actually bought two cases for my G4. I bought an Otterbox-like case, expecting to use this one, and a sleeker case that offered far less protection than I am usually comfortable with. I put the first case on initially, but after a few hours of contemplation I decided to be brave and put the second case on along with the screen protector. So far I'm very happy with my decision, I haven't had the (unintentional) opportunity to test the durability of the case by launching my phone across the room yet (which did happen to my previous phone, luckily it was plenty protected by an Otterbox), but I am enjoying the feel and appearance of this case far more and I'm certain this case is durable enough to protect my phone from small bumps, knocks, and drops. I assume a hard enough drop would crack the plastic shell of the case, but then again I suppose that's what the case is for, and it's cheap enough I'll just order another if that happens. As long as the glass screen protector is as tough as it claims to be, I'm confident in the current protection of my phone.
I have an amFilm tempered glass screen protector and love it. The size is absolutely perfect and have had zero issues with touch sensitivity. It also fits flawlessly with every case I've put on the phone. (I bought like five different cases because I'm indecisive and perfectionist when cases are concerned)
http://www.amazon.com/gp/product/B00XJS2O0E?psc=1&redirect=true&ref_=oh_aui_detailpage_o02_s00
I use this one. It comes witha lifetime warranty. http://www.amazon.com/Protector-Tempered-T-moible-Lifetime-Warranty/dp/B00XJS2O0E
I did a little bit of research before buying mine and from what I've read, most tempered glass screen protectors are more or less equal in quality as long as they have an oleophobic coating, which resists fingerprints.
Diztronic. Easy to access the battery when you need it. Not so thin that it seems useless. I can't decide if I like the feel of the case or not, but at least it doesn't pick up lint (some really cheap TPU ones did for me a while back). The NeoHybrid is a nice slightly heavier duty case, but is a huge PITA to take off. Not good if you frequently or quickly change batteries.
I bought this glass: http://www.amazon.com/Protector-Tempered-T-moible-Lifetime-Warranty/dp/B00XJS2O0E/ and it fits well, no problems getting it on (a little hard to line up, but that's a given for nearly every near-perfect-fit-anything for me. I really don't think I NEED it, but I get paranoid wiping away at the screen all the time.
LG G4 Screen Protector Glass, amFilmⓇ 0.2mm 2.5D Tempered Gl... http://www.amazon.com/dp/B00XJS2O0E/ref=cm_sw_r_udp_awd_xbIFvbWBET09G
I use this one, Its nice and smooth, easy install http://www.amazon.com/gp/product/B00XJS2O0E?ref_=pd_ybh_10