Verizon Samsung Galaxy S4 Root, Recovery and ROMs
RootThe Samsung Galaxy S4 has only been out on Verizon a few days, and it's already been rooted. The http://www.sxtpdevelopers.com site already has a good forum going. Despite Verizon's attempt to harden the kernel to prevent the Motochopper exploit that is used from working, the exploit works by first loading an earlier version of the kernel, then running the exploit, then reloading the latest kernel.
RecoveryThere's a new set of tools for flashing kernels and recoveries that works around the locked bootloader on the Galaxy S4 called Loki. While I've not downloaded the source code yet to use it, it's my understanding that the recovery installed by GooManager uses this set of tools.
So, after you've got root, go get GooManager and you can install the Team Win Recovery Project (TWRP) recovery.
The sex tape developer's site also has a CWM recovery under development as discussed in this forum. It looks like in order to try this one, you'll need to download and build the Loki tools.
ROMsPerhaps the most important ROM of all is out at the sex tape developer's site, the stock unrooted original ROM. At this point, there are several other proof of concept ROMs under development there as well, but nothing that looks ready to really use yet.
Of course, if you want to go looking for ROMs, a good place to go is always the xda-developers.com site. Today, the Verizon Samsung Galaxy S4 forum is at the top of the list! So far, I've only one ROM here, a stock rooted odexed and deodexed.
The kernel from Faux123 is out for all US and International versions of the Galaxy S4. I just downloaded from this thread.
Similar to getting Google Wallet working on the Samsung Galaxy S3, the S4 requires a /system/build.prop hack, flashing a deodexed ROM, loading the Xposed framework, and applying an Xposed framework patch.
This XDA thread was started for T-Mobile, but can be followed except that before beginning you will want to download a deodexed ROM for your carrier of the device, like the Verizon one mentioned in this thread from XDA Developers. Basically, this will make your phone look like a Sprint Galaxy S4 device, which has access to the app. Once the app is installed and working, you can revert your build.prop back to the original.