OK, Seriously—What phone should I get right now?

A little information...

This will be, somehow, my first smartphone purchase. I'd consider myself on the higher end of technological understanding, but years of not wanting to be contacted at all times and simply dissatisfied with the smartphone market have kept me from upgrading ye olde cell phone.

I'm on Verizon's network.

I'm familiar with my Nexus 7 and I really like the state of Android, and dislike a number of things about Apple's approach to interface and app publishing. So my mind's made up in that regard. The question is: what phone?

I know Verizon isn't offering the HTC One yet, but I also don't know if it's my best option, either. I spend quite a bit of time each week out in the woods (8 hours or more a day), where the lack of cell reception tends to DRAIN my current cell phone battery. (It gets very sporadic signal on clear days). So a phone with good reception and a STRONG battery — and good "airplane" (I guess?) modes is crucial.

I also require that it be fast and responsive. From playing with most of the phones in the Verizon store, it seems they're all FAIRLY up to snuff, but I want something that isn't going to crash when I want to stop what I'm doing and watch a Youtube video. I'm looking for something at least as powerful as the Nexus 7 in this regard... not necessarily more powerful, but on par with it.

Obviously, the nicer the camera the better, but I also have a DSLR so this isn't the most important area. Anything will be better than my current cell camera.

Another thing I REALLY want is the ability to take the phone back to stock Android or at least get as close as possible to that. I really don't like how some of these phones come with apps that you can't delete. (Maybe it's worth installing a fresh ROM?)

Other things I should be thinking about? What are my best bets? Should I spring for the relatively inexpensive Galaxy S3, or is the 4 really that much better? I've been considering the DROID RAZR series pretty seriously. How do the Galaxies and Razrs compare?

Thanks in advance!