Reddit reviews Hyperion Samsung Galaxy S4 5200mAh Extended Battery + Black Back Cover (Compatible with All Samsung Galaxy S 4 Models) Now with NFC/Google Wallet [18 Month Warranty]

Then I think you're leaning the right way. The GS4 lasts all day with moderate use from most reviews I've read. The SD card slot is a must for stock 16GB version, but I don't know how much the GE OS will take up on the hard drive.
If you're looking for expanded batteries, then I'd suggest these that were recommended by /u/moar_distractions:

• Zerolemon 7500mAh battery ($40)
  http://www.amazon.com/gp/product/B00CXZI3DQ/ref=oh_details_o00_s00_i00?ie=UTF8&psc=1
  
• Slightly more manageable 5200mAh ($25)
  http://www.amazon.com/Hyperion-Samsung-Extended-Compatible-Warranty/dp/B00BCK2G40/ref=sr_1_6?s=electronics&ie=UTF8&qid=1371040849&sr=1-6&keywords=galaxy+s4+battery
  
• A case for the Hyperion 5200 battery that looks pretty sick http://www.amazon.com/Hyperion-Samsung-Extended-HoneyComb-Packaging/dp/B00CXO09DY/ref=pd_sim_e_2
  
• Set of two standard size, supports NFC and Wallet, comes with a charger, looks promising to me ($25) http://www.amazon.com/Hyperion-Samsung-Batteries-Compatible-Warranty/dp/B00BCJWYMU/ref=sr_1_8?s=electronics&ie=UTF8&qid=1371040849&sr=1-8&keywords=galaxy+s4+battery
  
• 1 Hyperion standard size, with docking cradle that charges the extra battery (what sized cases fit?) ($30) http://www.amazon.com/Hyperion-Charging-Includes-Compatible-Warranty/dp/B00CP8EK1U/ref=pd_sim_e_3

Don't get a battery case. Get an extended battery and a replacement cover. They are thinner, cheaper, with more capacity for the size.

Hyperion Samsung Galaxy S4 5200mAh Extended Battery + Black Back Co... http://www.amazon.com/dp/B00BCK2G40/ref=cm_sw_r_udp_awd_IPRUtb120HHE9

[180 days warranty] ZeroLemon Samsung Galaxy S4 7500mAh Extended Ba... http://www.amazon.com/dp/B00CXZI4WQ/ref=cm_sw_r_udp_awd_8RRUtb00DEMT9

I personally reccomend the second link, I had it and loved it, it was just too thick for me. I didn't need the extra battery

Been using this combo since the S4 was released..


Battery:

http://www.amazon.com/Hyperion-Samsung-Extended-Compatible-Warranty/dp/B00BCK2G40

Case:

http://www.amazon.com/Hyperion-Samsung-Extended-HoneyComb-Packaging/dp/B00CXO09DY


EDIT: Fixed case link

Here's the link for the battery. Sorry, I was on mobile earlier. It does come with a cover.

I can think of times this would be helpful, long road trips where everyone might be fighting over one charger, long flights, camping. I just can't see myself having it permanently on my phone. Here are some other options I found quick on Amazon just in case people are interested. For me personally, I think I'm going to get a 2 pack of standard batteries that come with their own external charger. I can keep those in my backpack (or one in my pocket) and between the regular one and backup I can't see myself needing more.

• Slightly more manageable 5200mAh ($25)
  http://www.amazon.com/Hyperion-Samsung-Extended-Compatible-Warranty/dp/B00BCK2G40/ref=sr_1_6?s=electronics&ie=UTF8&qid=1371040849&sr=1-6&keywords=galaxy+s4+battery
  
• A case for the Hyperion 5200 battery that looks pretty sick
  http://www.amazon.com/Hyperion-Samsung-Extended-HoneyComb-Packaging/dp/B00CXO09DY/ref=pd_sim_e_2
  
• Set of two standard size, supports NFC and Wallet, comes with a charger, looks promising to me ($25)
  http://www.amazon.com/Hyperion-Samsung-Batteries-Compatible-Warranty/dp/B00BCJWYMU/ref=sr_1_8?s=electronics&ie=UTF8&qid=1371040849&sr=1-8&keywords=galaxy+s4+battery
  
• 1 Hyperion standard size, with docking cradle that charges the extra battery (what sized cases fit?) ($30)
  http://www.amazon.com/Hyperion-Charging-Includes-Compatible-Warranty/dp/B00CP8EK1U/ref=pd_sim_e_3
  
  Does anyone have any experience with these Hyperion brands? They all come with an 18 month warranty which sounds pretty sweet.

This battery has NFC.

This which Is what I will most likely buy

http://www.amazon.com/Hyperion-Samsung-Extended-HoneyComb-Packaging/dp/B00CXO09DY/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=1XH2Q6A84RDVZ&coliid=I2VATK67SCNVDJ

also the battery which is 5200mah sold seperately

link: http://www.amazon.com/Hyperion-Samsung-Extended-Compatible-Warranty/dp/B00BCK2G40/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=1XH2Q6A84RDVZ&coliid=I2IM67WBI29BJJ

under 50 dollars for a case and a larger battery.

I have a 5200mAh Hyperion battery going on a year old. No issues. http://www.amazon.com/Hyperion-Extended-Compatible-Carriers-compatible/dp/B00BCK2G40/ref=pd_sim_cps_17?ie=UTF8&refRID=0YSV29A2S0C32K68SRJ2

You do realize that there are after market batteries you can can buy that are a lot bigger and last a lot longer ?

http://www.amazon.com/Hyperion-Samsung-Extended-Compatible-Warranty/dp/B00BCK2G40 (just an example)

I got this one for my galaxy s4, which actually holds more juice than most stock laptop batteries. It made the battery last about 3 times longer but it also made it 3 times heavier. It weighs about as much as 1 cup of water (8fl oz). I think it's worth it to know that even if you're away from a charger for 2 nights you'll still have battery left, and that's without conserving. If I underclock my phone cpu, turn down screen brightness, and turn off mobile internet and only text and make calls, my phone would probably last a week. If you're looking to only use about 50% of your battery life per day, I would recommend the slightly lighter version.

Those who dont care already went with Apple or took their money to Samsung, whose crushing domination with Android mobiles speaks loud enough about how attractive expandable storage and replacable/upgradable batteries really are. Especially when the cloud is unreliable/slow, bandwidth costly and the base battery life is a common source of complaints. I mean, look at the autonomy of this monster.

On Android, iDevices are not the leader to challenge, Samsung devices are, and it's disturbing how many OEMs aren't even trying to make their devices attractive next to the default selection from Samsung.