Requirements:
charge Galaxy S4, iPhone 5, Nexus 7 and iPad mini daily (total battery: 2600 mAh + 1500 mAh +4000 mAh + 4500mAh = 12600 mAh per day
what battery and solar panels might work best? Any recommendations on where to buy?
I wanted something bigger than what you are asking for, but maybe it is still interesting to you. I did look at off-grid solar packages, but I didn't want to do a fixed installation and I wanted something that the rest of my family could deal with hooking up. I wanted something that could run a full sized refrigerator for almost a day (actually run it for half a day, then let it slowly warm up for the next 8-12 hours at the worst case). I also wanted something that I could, in a pinch, connect to solar to extend the runtime.
I ended up buying a Goal Zero Yeti 1250 but not their solar panels which are nice and portable, but terrible on a $/watt basis. I picked up two Helios 6T-240 mono crystalline solar panels (B grade off eBay) and the associated mc4 cables to hook them up in parallel and attached the appropriate anderson connector to be able to charge the Yeti 1250 through its anderson input port. That Anderson PP45 port in the front of the Yeti 1250 goes to their charge controller which can handle 240 watts. With two nominally rated 240 watt mono-crystalline solar panels, even on a cloudy day, I can hit the 200 watt or so level for hours. So for roughly 5-6 hours (yearly average for my latitude), there are 220+ watts coming into the Yeti 1250. My refrigerator cycles on and off, so it is important that the Yeti 1250 can take the surge requirements. However, on a ongoing basis, it is roughly 75 watts, so the Yeti 1250 can power it for over 12 hours. On a normal basis, the Yeti 1250 is plugged into the wall electricity through their supplied 80 watt charger because hooking up the solar is cumbersome (not a fixed installation). But if I had to, I could conceivably run the refrigerator on an ongoing basis with solar power in the summer (7-8 hours of charging @ 220+ watts while drawing 75 watts). Total cost was about $1500, but that is with careful shopping. The panels were B grade because the aluminum frame was slightly bent. No apparent affect on the operation of the panel itself.
I have also tried running my clothes washer off of it which works well. It is possible to daisy chain more than one Yeti 1250 together or daisy chain additional 12v batteries. The 12v battery inside is a standard 100Ah battery and can be replaced with a generic replacement. Also, it is possible to pack up the Yeti 1250 and stick the panels on top of my SUV and drive off with it. The full sized panels are cumbersome and heavy - 3' x 5' in size, so it's not a "normal" thing to do.
It is possible to buy all the components to replicate a Yeti 1250 for far cheaper and there are other alternatives, but it is hard to get it all put together in a single package that is as nice and user friendly.
I have tried charging my Tesla off of the Yeti 1250 more on a lark, but as usual for this kind of install, there is a ground fault. I suspect if I grounded the setup then it would work, but at the very best I'd get a kilowatt into the car. It might help with vampire drain.