So safe strap will help unlock and root, can I then flash a Google play edition ROM or am I limited to safe strap ROMs?
Moto X/Nexus 5
ROMs must be safestrap compatible.
All VZW GS4s can be rooted as far as I'm aware, but the bootloader is locked and encrypted so that it cannot be unlocked. Root itself will allow you to run root apps and remove bloatware, etc, but the reason the latter part is important is for the ability to install a custom recovery partition and install custom firmware (ROMs).
A workaround was discovered for the *ORIGINAL* build on the Verizon GS4 (I545VRUAMDK) called "Loki" which enabled users to install ROMs despite the locked bootloader. (ROMs had to be compatible with Loki). Unfortunately, this no longer works on all future builds of the VZW GS4...so any phone that has been upgraded or purchased recently can no longer use this method to install ROMs.
What Safestrap does is circumvent this by essentially running a virtual instance of Android that you can boot to, without touching the existing OS (paraphrasing and simplifying here for noobs). It's probably more suited for "expert" users, and yes, the ROMs have to be compatible with this method of install (check the ROM OP and/or thread...but as far as I know, there are
no SS compatible AOSP or CM ROMs). Also, because it has to use the user partition to install the ROMs (/sdcard), you will lose a considerable amount of available storage on the device. If you want more information on safestrap, please see the original XDA thread here:
[RECOVERY LOCKED] Safestrap Recovery v3.71 [2013-12-27 EXFAT Fix] - xda-developers
I definitely consider myself lucky to still have my rooted MDK Verizon GS4.