Tempered glass screen protector on mine. When using my black leather back, no case. If I put the gray plastic on, which now has wireless charging, seems with a case it doesn't work. So, been going without on that one also.
I have 3 leather backs. Blue, Orange, and Black. (No case used, but I'm thinking about getting the rubber bumper that goes around the outside of the phone.) All 3 have Qi stickers installed on them and I have 2 Qi chargers. One at work and one beside my bed. For me, Qi charging is a must! Love it!
Other than that, I need a car "docking" station, but haven't found one that I like yet. (I have docking in quotes because I really don't care if it has charging capabilities or not.)
An extra battery is important as is an external charger. I got the battery and charger from LG for free along with the blue leather back.
A nice set of bluetooth headphones is important when working out for me.
Other than that, I really don't have any other must haves for my phone.