Try all the phones you're considering for as long as you can. I wouldn't be upset with any of their LTE offerings (except maybe the SIII LTE at that price). I'm leaning towards the One right now, but by the time I upgrade this summer I might want an S4.
I've been loving my Galaxy Note 2 since March. If you don't mind how large it is in your hand, it has a great screen for viewing and even multitasking with the split screen. And it's fast, plus I've even started picking up T-mobile's new LTE signal here in Portland in the past week - superfast.