I have sprint and have zero issues with service. I have spark LTE here in columbus and when i travel occasionally ill get 3g in some areas but its fast enough to do what I need to do.
I'll say the spigen cases are amazing. I had an 8 dollar spigen TPU case on my note 3 from amazon for a year or so. I dropped my phone a ton and never had any issues. I ran over my phone with my crv... The case did not protect against that...
I use this. Best case for protection and slimness.
http://www.amazon.com/Caseology-Samsung-Absorbent-T-mobile-Unlocked/dp/B00OM90E7Y/ref=sr_1_5?ie=UTF8&qid=1420489935&sr=8-5&keywords=Caseology+note+4